Full text of "soil analysis"

The Chemistry

Ol SoiiS Second E

Second Edition

Garrison Sposito

The Chemistry of Soils

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The Chemistry of Soils

Second Edition

Garrison Sposito

OXFORD

UNIVERSITY PRESS

2008

OXFORD

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Library of Congress Cataloging- in -Publication Data

Sposito, Garrison, 1939—

The chemistry of soils / Garrison Sposito.

p. cm.

Includes bibliographical references and index.

ISBN 978-0-19-531369-7

1. Soil chemistry. I. Title.

S592.5.S656 2008

631.4'l— dc22 2007028057

135798642

Printed in the United States of America
on acid-free paper

For Mary
'6 tl KaXov (piXov dei

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Preface

This book is intended for use by scientists and engineers in their research or in
their professional practice, and for use as a textbook in one-semester or one-
quarter courses on soil chemistry or biogeochemistry. A background in basic
soil science as found, for example, in Introduction to the Principles and Practice
of Soil Science by R. E. White, Soils by William Dubbin, or Soils: Genesis and
Geomorphology by Randall Schaetzl and Sharon Anderson is assumed on the
part of the reader. An understanding of chemistry and calculus at an elemen-
tary level also is necessary, although the latter topic is in fact applied very spar-
ingly throughout the text. Familiarity with statistical analysis is of considerable
benefit while solving some of the problems accompanying the text.

The general plan of the book is to introduce the principal reactive com-
ponents of soils in the first four chapters, then to describe important soil
chemical processes in the next six. One hopes that the reader will notice that
a conscious effort has been made throughout the text to blur somewhat the
distinction between soil chemistry and soil microbiology. The final pair of
chapters discusses applications of soil chemistry to the two most important
issues attending the maintenance of soil quality for agriculture: soil acidity and
soil salinity. These two chapters are not intended to be comprehensive reviews,
but instead to serve as guides to the soil chemistry underlying the topics
discussed in more specialized courses or books on soil quality management.

A brief appendix on le Systeme International d'Unites (SI units) and physi-
cal quantities used in soil chemistry is provided at the end of the book. Readers
are advised to review this appendix and work the problems in it before beginn-
ing to read the book itself, not only as a prequel to the terminology appearing

viii Preface

in the text, but also as an aid to evaluating the status of their understanding
of introductory chemistry. The 180 problems following the chapters in this
book have been designed to reinforce or extend the main points discussed and
thus are regarded as an integral part of the text. No reader should be satisfied
with her or his understanding of soil chemistry without undertaking at least a
substantial portion of these problems. In addition to the problems, an anno-
tated reading list at the end of each chapter is offered to those who wish to
explore in greater depth the subject matter discussed. Both the problems and
the reading lists should figure importantly in any course of university lectures
based on this book.

Acknowledgments

I must thank Angela Zabel for her excellent preparation of the typescript of
this book and Cynthia Borcena for her most creative preparation of its figures.
I must also express gratitude to Stephen Judge for initially suggesting that
I write a soil chemistry textbook, to Harvey Doner and John Hsu for providing
lengthy commentary on and corrections to its first edition (now nearly 20 years
old), and to Kirk Nordstrom for his generosity in sharing material related to
aluminum geochemistry that strongly influenced the writing of Chapter 11.
Thanks also to Kideok Kwon, Sung-Ho Park, and Rebecca Sutton for providing
original artwork for some of the figures, and to Teri Van Dorston for her able
assistance in providing an image of the painting that adorns the front cover
of this book. Finally, I must express my great indebtedness to two of my
Berkeley colleagues — Bob Hass and Tony Long — humanists whose example
and perspectives have influenced my writing in ways I could scarcely have
imagined two decades ago.

Berkeley, California
May 2007

Cover art: Grant Wood, Young Corn, 1931. Oil on Masonite panel,
24x29 7/8 in. Collection of the Cedar Rapids Community School District, on
loan to the Cedar Rapids Museum of Art. Used with permission of the owner.

Contents

The Chemical Composition of Soils 3

1.1 Elemental Composition 3

1.2 Metal Elements in Soils 8

1.3 Solid Phases in Soils 11

1.4 Soil Air and Soil Water 16

1.5 Soil Mineral Transformations 17
For Further Reading 20
Problems 2 1
Special Topic 1: Balancing Chemical

Reactions 25

Soil Minerals 28

2.1 Ionic Solids 28

2.2 Primary Silicates 36

2.3 Clay Minerals 41

2.4 Metal Oxides, Oxyhydroxides, and

Hydroxides 49

2.5 Carbonates and Sulfates 54
For Further Reading 56
Problems 57
Special Topic 2: The Discovery of the

Structures of Clay Minerals 59

Contents

Soil Humus 65

3.1 Biomolecules 65

3.2 Humic Substances 70

3.3 Cation Exchange Reactions 72

3.4 Reactions with Organic Molecules 77

3.5 Reactions with Soil Minerals 82
For Further Reading 85
Problems 86
Special Topic 3: Film Diffusion Kinetics in

Cation Exchange 9 1

The Soil Solution 94

4.1 Sampling the Soil Solution 94

4.2 Soluble Complexes 96

4.3 Chemical Speciation 101

4.4 Predicting Chemical Speciation 104

4.5 Thermodynamic Stability Constants 1 10
For Further Reading 113
Problems 1 14

Mineral Stability and Weathering 1 19

5.1 Dissolution Reactions 119

5.2 Predicting Solubility Control: Activity-Ratio

Diagrams 125

5.3 Coprecipitated Soil Minerals 130

5.4 Predicting Solubility Control: Predominance

Diagrams 133

5.5 Phosphate Transformations in Calcareous Soils 135
For Further Reading 139
Problems 140

Oxidation-Reduction Reactions 144

6.1 Flooded Soils 144

6.2 Redox Reactions 148

6.3 The Redox Ladder 154

6.4 Exploring the Redox Ladder 159

6.5 pE-pH Diagrams 162
For Further Reading 165
Problems 166
Special Topic 4: Balancing Redox

Reactions 169

Special Topic 5: The Invention of the pH Meter 171

Soil Particle Surface Charge 174

7.1 Surface Complexes 174

7.2 Adsorption 179

7.3 Surface Charge 181

Contents xi

7.4 Points of Zero Charge 183

7.5 Schindler Diagrams 188
For Further Reading 190
Problems 191

8 Soil Adsorption Phenomena 195

8.1 Measuring Adsorption 195

8.2 Adsorption Kinetics and Equilibria 197

8.3 Metal Cation Adsorption 203

8.4 Anion Adsorption 206

8.5 Surface Redox Processes 209
For Further Reading 214
Problems 214

9 Exchangeable Ions 219

9.1 Soil Exchange Capacities 219

9.2 Exchange Isotherms 223

9.3 Ion Exchange Reactions 226

9.4 Biotic Ligand Model 230

9.5 Cation Exchange on Humus 233
For Further Reading 238
Problems 239

10 Colloidal Phenomena 244

10.1 Colloidal Suspensions 244

10.2 Soil Colloids 248

10.3 Interparticle Forces 250

10.4 The Stability Ratio 255

10.5 Fractal Floccules 261
For Further Reading 266
Problems 267
Special Topic 6: Mass Fractals 271

11 Soil Acidity 275

11.1 Proton Cycling 275

11.2 Acid-Neutralizing Capacity 279

11.3 Aluminum Geochemistry 282

11.4 Redox Effects 286

11.5 Neutralizing Soil Acidity 288
For Further Reading 290
Problems 291
Special Topic 7: Measuring pH 293

12 Soil Salinity 296

12.1 Saline Soil Solutions 296

12.2 Cation Exchange and Colloidal

Phenomena 298

Contents

12.3

Mineral Weathering

12.4

Boron Chemistry

12.5

Irrigation Water Quality

For Further Reading

Problems

302
305
308
311
312

Appendix: Units and Physical Constants in Soil Chemistry 316

For Further Reading 319

Problems 319

Index 321

The Chemistry of Soils

Right thinking is the greatest excellence,
and wisdom is to speak the truth

and act in accordance with Nature,
while paying attention to it.

— Heraclitus of Ephesus

Now we give place to the genius of soils,
the strength of each, its hue,
its native power for bearing.

— Vergil, Georgics II

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The Chemical Composition of Soils

1.1 Elemental Composition

Soils are porous media created at the land surface through weathering pro-
cesses mediated by biological, geological, and hydrological phenomena. Soils
differ from mere weathered rock, however, because they show an approxi-
mately vertical stratification (the soil horizons) that has been produced by the
continual influence of percolating water and living organisms. From the point
of view of chemistry, soils are open, multicomponent, biogeochemical sys-
tems containing solids, liquids, and gases. That they are open systems means
soils exchange both matter and energy with the surrounding atmosphere,
biosphere, and hydrosphere. These flows of matter and energy to or from soils
are highly variable in time and space, but they are the essential fluxes that cause
the development of soil profiles and govern the patterns of soil quality.

The role of soil as a dynamic reservoir in the cycling of chemical elements
can be appreciated by examining tables 1.1 and 1.2, which list average mass
concentrations of important nonmetal, metal, and metalloid chemical ele-
ments in continental crustal rocks and soils. The rock concentrations take into
account both crustal stratification and the relative abundance of sedimentary,
magmatic, and metamorphic subunits worldwide. The soil concentrations
refer to samples taken approximately 0.2 m beneath the land surface from
uncontaminated mineral soils in the conterminous United States. These lat-
ter concentration data are quite comparable with those for soils sampled
worldwide. The average values listed have large standard deviations, however,
because of spatial heterogeneity on all scales.

4 The Chemistry of Soils

Table 1.1

Mean content (measured in milligrams per kilogram) of nonmetal elements in
crustal rocks and United States soils.

Element

Crust 3

Soil b

Element

Crust 3

Soil b

757

260

1990

16,000

697

1200

2000

472

100

472,000

490,000

0.12

0.26

a Wedepohl, K. H. (1995) The composition of the continental crust. Geochim. Cosmochim. Acta
59: 1217.

Schacklette, H. T., and J. G. Boerngen. (1984) Element concentrations in soils and other sur-
ficial materials of the conterminous United States. U.S. Geological Survey Professional Paper
1270.

Table 1.2

Mean content (measured in milligrams per kilogram) of metal and metalloid
elements and their anthropogenic mobilization factors (AMFs).

Element

Crust 3

Soil 1

AMF C

Element Crust 3

Soil b

AMF C

632

2.4

0.6

115

23600

5900

1.7

5.2

22000

4400

333

120

79600

47000

203

180

288000

310000

1.1

0.6

21400

15000

0.07

0.05

185

38500

9200

0.1

0.2

112

4010

2400

0.9

0.3

0.5

246

126

273

3.4

4.0

716

330

584

440

43200

18000

0.04

0.06

342

14.8

127

1.7

2.3

a Wedepohl, K. H. (1995) The composition of the continental crust. Geochim. Cosmochim. Acta
59:1217.

Schacklette, H. T., and ). G. Boerngen. (1984) Element concentrations in soils and other sur-
ficial materials of the conterminous United States. U.S. Geological Survey Professional Paper
1270.

C AMF = mass extracted annually by mining and fossil fuel production -=- mass released annu-
ally by crustal weathering and volcanic activity. Data from Klee, R. J., and T. E. Graedel. (2004)
Elemental cycles: A status report on human or natural dominance. Annu. Rev. Environ. Resour.
29:69.

The Chemical Composition of Soils 5

The major elements in soils are those with concentrations that exceed
100 mgkg , all others being termed trace elements. According to the data in
tables 1.1 and 1.2, the major elements include O, Si, Al, Fe, C, K, Ca, Na, Mg,
Ti, N, S, Ba, Mn, P, and perhaps Sr and Zr, in decreasing order of concentra-
tion. Notable among the major elements is the strong enrichment of C and
N in soils relative to crustal rocks (Table 1.1), whereas Ca, Na, and Mg show
significant depletion (Table 1.2). The strong enrichment of C and N is a result
of the principal chemical forms these elements assume in soils — namely, those
associated with organic matter. The average C-to-N, C-to-P, and C-to-S ratios
(8, 61, and 13 respectively) in soils, indicated by the data in Table 1.1, are very
low and, therefore, are conducive to microbial mineralization processes, fur-
ther reflecting the active biological milieu that distinguishes soil from crustal
rock.

The major elements C, N, P, and S also are macronutrients, meaning they
are essential to the life cycles of organisms and are absorbed by them in signifi-
cant amounts. The global biogeochemical cycles of these elements are therefore
of major interest, especially because of the large anthropogenic influence they
experience. Mining operations and fossil fuel production, for example, com-
bine to release annually more than 1000 times as much C and N, 100 times
as much S, and 10 times as much P as is released annually worldwide from
crustal weathering processes. In soils, these four elements undergo biological
and chemical transformations that release them to the vicinal atmosphere,
biosphere, and hydrosphere, as illustrated in Figure 1.1, a flow diagram that
applies to natural soils at spatial scales ranging from pedon to landscape. The
two storage components in Figure 1.1 respectively depict the litter layer and
humus, the organic matter not identifiable as unaltered or partially altered
biomass. The microbial transformation of litter to humus is termed humi-
fication. The content of humus in soils worldwide varies systematically with
climate, with accumulation being favored by low temperature and high pre-
cipitation. For example, the average humus content in desert soils increases by
about one order of magnitude as the mean annual surface temperature drops
fivefold. The average humus content of tropical forest soils increases approx-
imately threefold as the mean annual precipitation increases about eightfold.
In most soils, the microbial degradation of litter and humus is the process
through which C, N, S, and P are released to the contiguous aqueous phase
(the soil solution) as inorganic ions susceptible to uptake by the biota or loss
by the three processes indicated in Figure 1.1 by arrows outgoing from the
humus storage component.

Important losses of C from soils occur as a result of leaching, erosion,
and runoff, but most quantitative studies have focused on emissions to the
atmosphere in the form of either CO2 or CH4 produced by respiring microor-
ganisms. The CO2 emissions do not arise uniformly from soil humus, but
instead are ascribed conventionally to three humus "pools": an active pool,
with C residence times up to a year; a slow pool, with residence times up to a
century, and a passive pool, with residence times up to a millennium. Natural

The Chemistry of Soils

humifi-

▲

LITTER

HUMUS

erosion

cation

runoff

leaching

Figure 1.1. Flow diagram showing storage components (boxes) and transfers (arrows)
in the soil biogeochemical cycling of C, N, P, and S.

soils can continue to accumulate C for several millennia, only to lose it over
decades when placed under cultivation. The importance of this loss can be
appreciated in light of the fact that soils are the largest repository of nonfos-
sil fuel organic C on the planet, storing about four times the amount of C
contained in the terrestrial biosphere.

The picture for soil N flows is similar to that for soil C, in that humus
is the dominant storage component and emissions to the atmosphere are an
important pathway of loss. The emissions send mainly N2 along with N2O
and NH3 to the atmosphere. The N2O, like CO2 and CH4, is of environmental
concern because of its very strong absorption of terrestrial infrared radia-
tion (greenhouse gas). Unlike the case of CO2 and CH4, however, the source
of these gases is dissolved inorganic N, the transformation of which is termed
denitrification when N2 and N2O are the products, and ammonia volatilization
when NH3 is the product. Denitrification is typically mediated by respiring
microorganisms, whereas ammonia volatilization results from the deprotona-
tion of aqueous NHJ" (which itself may be bacterially produced) under alkaline
conditions. Dissolved inorganic N comprises the highly soluble, "free-ion"
chemical species, NO^~, NO^, and NH4 , which can transform among them-
selves by electron transfer processes (redox reactions), be complexed by other
dissolved solutes, react with particle surfaces, or be absorbed by living organ-
isms, as illustrated in the competition diagram shown in Figure 1.2, which
pertains to soils at the ped spatial scale. Natural soils tend to cycle N with-
out significant loss through leaching (as NO^~), but denitrification losses can
be large if soluble humus, which is readily decomposed by microorganisms,
is abundant and flooding induces anaerobic conditions, thereby eliminating
O as a competitor with N for the electrons made available when humus is
degraded. Cultivated soils, on the other hand, often show excessive leaching
and runoff losses of N, as well as significant emissions — both of which are of

The Chemical Composition of Soils 7

major environmental concern — because of high inputs of nitrate or ammo-
nium fertilizers that artificially and suddenly increase inorganic N content.
A similar problem occurs when organic wastes with low C-to-N ratios are
applied to these soils as fertilizers, because rapid microbial mineralization of
such materials is favored.

Sulfur flows in soils that form outside arid regions or tidal zones can
be described as shown in Figure 1.1, with humus as the dominant reservoir
and losses through leaching, runoff, and emission processes. Mineralization of
organic S in humus usually produces S0 4 ~, which can be leached, react with
particle surfaces, or be absorbed by living organisms (Fig. 1.2). In flooded
soils, soluble H2S and other potentially volatile sulfides are produced under
microbial mediation from the degradation of humus or the reduction of sulfate
(electron transfer to sulfate to produce sulfide). They can be lost by emission
to the atmosphere or by precipitation along with ferrous iron or trace metals
as solid-phase sulfides. The competition for aqueous S0 4 ~ in soil peds thus
follows the paradigm in Figure 1.2, with the main differences from NO^~ being
the much stronger reactions between sulfate and particle surfaces and the
possibility of precipitation as a solid-phase sulfide, as well as emission to the
atmosphere, under flooded conditions.

Phosphorus flows in soils follow the diagram in Figure 1.1 with the impor-
tant caveat that inorganic P reservoirs — phosphate on particle surfaces and in
solid phases — can sometimes be as large as or larger than that afforded by
humus, depending on precipitation. Leaching losses of soil P are minimal, and
gaseous P emissions to the atmosphere essentially do not occur from natural

MICROBES

INORGANIC
COMPLEXES

FREE
CATION OR ANION

ORGANIC
COMPLEXES

PARTICLE
SURFACES

SOLID PHASES

Figure 1.2. Competition diagram showing biotic and abiotic sources/sinks for aque-
ous species (inner three boxes) in a soil ped. Coupling among the four sources/sinks is
mediated by the free ionic species of an element.

8 The Chemistry of Soils

soils. Mineralization of humus and dissolution of P from solid phases both
produce aqueous P0 4 ~ or its proton complexes (e.g., H2PO4), depending
on pH, and these dissolved species can be absorbed by living organisms or
lost to particle surfaces through adsorption reactions, which are yet stronger
than those of sulfate, and through precipitation, along with Ca, Al, or Fe, as a
solid-phase phosphate, again depending on pH. As is the case with N, fertilizer
additions and organic waste applications to soils can lead to P losses, mainly
by erosion, that pose environmental hazards.

Even this brief summary of the soil cycles of C, N, S, and P can serve to
illustrate their biogeochemical similarities in the setting provided by Figures
1.1 and 1.2. Humus is their principal reservoir (with P sometimes as an excep-
tion), and all four elements become oxyanions (C0 3 ~, NO^~, S0 4 ~, P0 4 ~,
and their proton complexes) when humus is mineralized by microorganisms
under aerobic conditions at circumneutral pH. The affinity of these oxyanions
for particle surfaces, as well as their susceptibility to precipitation with metals,
has been observed often to increase in the order NO^~ < S0 4 ~ < C0 3 ~ <JC
P0 4 ~. This ordering is accordingly reversed for their potential to be lost from
soils by leaching or runoff processes, whereas it remains the same for their
potential to be lost by erosion processes.

1.2 Metal Elements in Soils

Table 1.2 lists average crustal and soil concentrations of 27 metals and three
metalloids (Si, As, and Sb) along with their anthropogenic mobilization factors
(AMFs). The value of AMF is calculated as the mass of an element extracted
annually, through mining operations and fossil fuel production, divided by
the mass released annually through crustal weathering processes and volcanic
activity, with both figures being based on data obtained worldwide. If AMF is
well above 10, an element is said to have significant anthropogenic perturba-
tion of its global biogeochemical cycle. A glance along the fourth and eighth
columns in Table 1.2 reveals that, according to this criterion, the transition
metals Cr, Ni, Cu, Zn, Mo, and Sn; the "heavy metals" Ag, Cd, Hg, and Pb; and
the metalloids As and Sb have significantly perturbed biogeochemical cycles.
Not surprisingly, these 12 elements also figure importantly in environmental
regulations.

Metal elements are classified according to two important characteristics
with respect to their biogeochemical behavior in soils and aquatic systems. The
first of these is the ionic potential (IP), which is the valence of a metal cation
divided by its ionic radius in nanometers. Metal cations with IP < 30 nm
tend to be found in circumneutral aqueous solutions as solvated chemical
species {free cations); those with 30 < IP < 100 nm tend to hydrolyze read-
ily in circumneutral waters; and those with IP > 100 nm tend to be found as
oxyanions. As examples of these three classes, consider Na + (IP = 9.8 nm -1 ),
A1 3+ (IP = 56nm- 1 ),andCr 6+ (IP = 231 nm -1 ). (SeeTable2.1 for alistingof

The Chemical Composition of Soils 9

ionic radii used to calculate IP.) If a metal element has different valence states,
it may fall into different classes: Cr + (IP = 49 nm ) hydrolyzes, whereas it
has just been shown that hexavalent Cr forms an oxyanion species in aqueous
solution. The physical basis for this classification can be understood in terms
of coulomb repulsion between the metal cation and a solvating water molecule
that binds to it in aqueous solution through ion— dipole interactions. If IP is
low, so is the positive coulomb field acting on and repelling the protons in
the solvating water molecule; but, as IP becomes larger, the repulsive coulomb
field becomes strong enough to cause one of the water protons to dissoci-
ate, thus forming a hydroxide ion. If IP is very large, the coulomb field then
becomes strong enough to dissociate both water protons, and an oxyanion
forms instead.

Evidently any monovalent cation with an ionic radius larger than 0.033 nm
will be a solvated species in aqueous solution, whereas any bivalent cation will
require an ionic radius larger than 0.067 nm to be a solvated species. The alkali
metal in Table 1.2 with the smallest cation is Li (ionic radius, 0.076 nm) and
the alkaline earth metal with the smallest cation is Be (ionic radius, 0.027 nm),
followed by Mg (ionic radius, 0.072 nm).Thus alkali and alkaline earth metals,
with the notable exception of Be, will be free cations in circumneutral aqueous
solutions. The same is true for the monovalent heavy metals (e.g., Ag + ) and the
bivalent transition metals and heavy metals (e.g., Mn + and Hg + ), although
the bivalent transition metals come perilously close to the IP hydrolysis thresh-
old. Trivalent metals, on the other hand, tend always to be hydrolyzed [e.g.,
Al 3+ , Cr 3+ , and Mn 3+ (IP = 46 nm -1 )], and quadrivalent or higher valent
metals tend to be oxyanions. The soluble metal species in circumneutral waters
are either free cations or free oxyanions, whereas hydrolyzing metals tend to
precipitate as insoluble oxides or hydroxides. Thus, falling into the middle IP
range (30-100 nm ) is the signature of metal elements that are not expected
to be soluble at circumneutral pH.

The second important characteristic of metal elements is their Class A or
Class B behavior. A metal cation is Class A if (1) it has low polarizability
(a measure of the ease with which the electrons in an ion can be drawn
away from its nucleus) and (2) it tends to form stronger complexes with O-
containingligands [e.g., carboxylate (COO - ), phosphate, or a water molecule]
than with N- or S-containing ligands. A metal is Class B if it has the opposite
characteristics. If a metal is neither Class A nor Class B, it is termed borderline.
The Class B metals in Table 1 .2 are the heavy metals Ag, Cd, Hg, and Pb, whereas
the borderline metals are the transition metals Ti to Zn, along with Zr, Mo,
and Sn, each of which can behave as Class A or Class B, depending on their
valence and local bonding environment (stereochemistry). All the other metals
in Table 1.2 are Class A. We note in passing that Class A metals tend to form
strong hydrophilic (water-loving) complexes with ligands in aqueous solution
through ionic or even electrostatic bonding, whereas Class B metals tend to
form strong lipophilic (fat-loving) complexes with ligands in aqueous solution
through more covalent bonding. Hydrophilic complexes seek polar molecular

10 The Chemistry of Soils

environments (e.g., cell surfaces), whereas lipophilic complexes seek nonpolar
environments (e.g., cell membranes) . These tendencies are a direct result of ( 1 )
the polarizability of a metal cation (with high polarizability implying a labile
"electron cloud," one that can be attracted toward and shared with a ligand)
and (2) the less polar nature of N- or S-containingligands, which makes them
less hydrophilic than O-containing ligands.

The description of metals according to these two characteristics can be
applied not only to understand the behavior of metals in terms of solubility and
complex formation, but also to predict their status as plant (and microbial)
toxicants (see the flow diagram in Fig. 1.3). For a given metal cation, if IP
< 30 nm -1 and the metal is Class A, then it is unlikely to be toxic (e.g.,
Ca 2+ ), except possibly at very high concentrations (e.g., Li + , Na + ). Moving
toward the right in Figure 1.3, we see that if IP > 100 nm , or if IP < 30
nm -1 and the metal is borderline, then it is quite possibly toxic, examples
being Cr 6+ in the first case and bivalent transition metal cations in the second
case. If, instead, 30 < IP < 100 nm , or the metal cation is Class B, then
it is very likely to be toxic, examples being Be + and Al + in the first case;
and Ag + , Hg + , along with the bivalent heavy metals in the second case. The
chemistry underlying these conclusions is simple: If a metal tends to hydrolyze
in aqueous solution or has covalent binding characteristics, it is very likely to
be toxic, whereas if it tends to be solvated in aqueous solution and has ionic

Figure 1.3. Flow diagram (beginning at upper left corner) for the toxicological classi-
fication of a metal cation at circumneutral pH using the criteria of ionic potential (IP)
and Class A or B character.

The Chemical Composition of Soils 11

or electrostatic binding characteristics, it is not as likely to be toxic. Toxicity
is thus associated with insoluble metal cations and with those that tend to
form covalent bonds in complexes with ligands. The first property evidently
reflects low abundance in aquatic systems and, therefore, the nonavailability
of a metal element as life evolved, whereas the second property is inimical to
the relatively labile metal cation binding that characterizes most biochemical
processes. Indeed, borderline metals become toxicants when they displace
Class A metals from essential binding sites in biomolecules, bonding to these
sites more strongly, and Class B metals are always toxicants, simply because
they can displace either borderline metals (which often serve as cofactors in
enzymes) or Class A metals from essential binding sites through much more
tenacious bonding mechanisms. Note that the large AMF values in Table 1.2
are associated with borderline and Class B metals, implying, unfortunately,
that human perturbations of metal biogeochemical cycles have enhanced the
concentrations of toxicant metals in soil and water environments.

1.3 Solid Phases in Soils

About one half to two thirds of the soil volume is made up of solid matter.
Of this material, typically more than 90% represents inorganic compounds,
except for Histosols (peat and muck soils), wherein organic material accounts
for more than 50% of the solid matter. The inorganic solid phases in soils
often do not have a simple stoichiometry (i.e., they do not exhibit molar ratios
of one element to another which are rational fractions), because they are
actually in a metastable state of transition from an inhomogeneous, irregular
structure to a more homogeneous, regular structure as a result of weathering
processes. Nonetheless, a number of solid phases of relatively uniform com-
position (minerals) has been identified in soils worldwide. Table 1.3 lists the
most common soil minerals along with their chemical formulas. Details of the
atomic structures of these minerals are given in Chapter 2.

According to Table 1 . 1, the two most abundant elements in soils are oxygen
and silicon, and these two elements combine chemically to form the 15 sili-
cates listed in Table 1 .3 . The first nine silicates in the table are termed primary
minerals because they are typically inherited from parent material, particularly
crustal rock, as opposed to being precipitated through weathering processes.
The key structural entity in these minerals is the Si— O bond, which is a more
covalent (and, therefore, stronger) bond than typical metal-oxygen bonds (see
Section 2.1). The relative resistance of any one of the minerals to decomposi-
tion by weathering is correlated positively with the Si-to-O molar ratio of its
fundamental silicate structural unit, as a larger Si-to-O ratio means a lesser
need to incorporate metal cations into the mineral structure to neutralize the
oxygen anion charge. To the extent that metal cations are so excluded, the
degree of covalency in the overall bonding arrangement will be greater and
the mineral will be more resistant to decomposition in the soil environment.

12 The Chemistry of Soils

Table 1.3

Common soil minerals.

Name

Chemical formula

Importance

Quartz

Si0 2

Abundant in sand and
silt

Feldspar

(Na,K)Al0 2 [Si0 2 ] 3

Abundant in soil that

CaAl 2 04[Si0 2 ]2

is not leached
extensively

Mica

K 2 Al 2 5 [Si 2 5 ]3Al4(OH)4

Source of K in most

K 2 Al 2 5 [Si 2 05]3(Mg,

temperate-zone soils

Fe) 6 (OH) 4

Amphibole

(Ca, Na, K) 2>3 (Mg, Fe,

Easily weathered to

Al) 5 (OH) 2

clay minerals and

[(Si,Al) 4 On] 2

oxides

Pyroxene

(Ca,Mg,Fe,Ti,Al) 2 (Si,
Al) 2 6

Easily weathered

Olivine

(Mg,Fe) 2 Si0 4

Easily weathered

Epidote

Ca 2 (Al,Fe)Al 2 (OH)Si 3 Oi 2

Tourmaline

NaMg 3 Al 6 B 3 Si 6 27

Highly resistant to

(OH,F) 4

chemical weathering

Zircon

ZrSi0 4

Rutile

TiO z

Kaolinite

Si 4 Al 4 O 10 (OH) 8

Smectite

M x (Si,Al) 8 (Al,Fe,

Abundant in soil clay

Illite

Mg) 4 O 20 (OH) 4

fractions as products

Vermiculite

M = interlayer cation

of weathering

Chlorite

0.4 < x < 2.0 = layer
charge

Allophane

Si r Al 4 6+2/ • nH 2 0,

Abundant in soils

1.6 < y < 4, n > 5

derived from

Imogolite

Si 2 Al 4 Oio • 5 H 2

volcanic ash deposits

Gibbsite

Al(OH) 3

Abundant in leached
soils

Goethite

FeOOH

Abundant Fe oxide in
temperate soils

Hematite

Fe 2 3

Abundant Fe oxide in
aerobic soils

Ferrihydrite

Fe 10 O 15 -9H 2 O

Abundant in
seasonally wet soils

Birnessite

M x Mn(IV) fl Mn(III) b A c 2

Most abundant Mn

M = interlayer cation,

oxide

x = b + 4c = layer

charge, a + b + c = 1

Lithiophorite

LiAl 2 (OH) 6 Mn(IV) 2 Mn(III)0

6 Found in acidic soils

Calcite

CaC0 3

Most abundant
carbonate

Gypsum

CaS0 4 • 2H 2

Most abundant sulfate

The Chemical Composition of Soils 13

For the first six silicates listed in Table 1.3, the Si-to-O molar ratios of their
fundamental structural units are as follows: 0.50 (quartz and feldspar, Si02),
0.40 (mica, S12O5), 0.36 (amphibole, Si^n), 0.33 (pyroxene, SiC^), and 0.25
(olivine, S1O4). The decreasing order of the Si-to-O molar ratio is the same as
the observed decreasing order of resistance of these minerals to weathering in
soils (see Section 2.2).

The minerals epidote, tourmaline, zircon, and rutile, listed in the middle
of Table 1.3, are highly resistant to weathering in the soil environment. Under
the assumption of uniform parent material, measured variation in the relative
number of single- crystal grains of these minerals in the fine sand or coarse silt
fractions of a soil profile can serve as a quantitative indicator of mass changes
in soil horizons produced by chemical weathering.

The minerals listed from kaolinite to gypsum in Table 1.3 are termed
secondary minerals because they nearly always result from the weathering
transformations of primary silicates. Often these secondary minerals are of clay
size and many exhibit a relatively poorly ordered atomic structure. Variability
in their composition through the substitution of ions into their structure (iso-
morphic substitution) also is noted frequently. The layer-type aluminosilicates,
smectite, illite, vermiculite, and chlorite, bear a net charge on their surfaces
( layer charge) principally because of this variability in composition, as shown
in Section 2.3. Kaolinite and the secondary metal oxides below it in the list —
with the important exception of birnessite — also bear a net surface charge,
but because of proton adsorption and desorption reactions, not isomorphic
substitutions. Birnessite, a layer-type Mn oxide, also bears a surface charge,
mainly because of vacancies in its structure (quantified by an x subscript in
the chemical formula) where Mn 4+ cations should reside. Secondary metal
oxides like gibbsite and goethite tend to persist in the soil environment longer
than secondary silicates because Si is more readily leached than Al, Fe, or Mn,
unless significant amounts of soluble organic matter are present to render
these latter metals more soluble.

Organic matter is, of course, an important constituent of the solid phase
in soils. The structural complexity of soil humus has thus far precluded the
making of a simple list of component solids like that in Table 1.3, but some-
thing can be said about the overall composition of humic substances — the
dark, microbially transformed organic materials that persist in soils (slow
and passive humus pools) throughout profile development. The two most
investigated humic substances are humic acid and fulvic acid. Their chem-
ical behavior is discussed in Section 3.2. Worldwide, the average chemical
formula for these two substances in soil is C185H191O90N10S (humic acid)
and C186H245O142N9S2 (fulvic acid). These two average chemical formu-
las can be compared with the average C-to-N-to-S molar ratio of bulk soil
humus, which is 140:10:1.3, and with the average chemical formula for ter-
restrial plants, which is C146H227O123N10. Relative to soil humus as a whole,
humic and fulvic acids are depleted in N. Their C-to-N molar ratio is 30%
to 50% larger than that of soil humus, indicating their greater resistance to

14 The Chemistry of Soils

net microbial mineralization. Relative to terrestrial plants, humic and ful-
vic acids are enriched in C but depleted in H. The depletion of H, from
roughly a 1.5:1 H-to-C molar ratio in plant material to roughly 1.3 in ful-
vic acid and 1.0 in humic acid, suggests a greater degree of aromaticity (e.g.,
H-to-C ratio is 1.0 in benzene, the prototypical aromatic organic molecule)
in the latter materials, which is consistent with their resistance to microbial
attack.

The 21 trace elements listed in Tables 1.1 and 1.2 seldom occur in soils as
separate mineral phases, but instead are found as constituents of host minerals
and humus. The principal ways in which important trace elements occur in
primary and secondary soil minerals are summarized in tables 1.4 and 1.5.
Table 1.5 also indicates the trace elements found typically in association with
soil humus. The chemical process underlying these trace element occurrences
is called coprecipitation. Coprecipitation is the simultaneous precipitation of
a chemical element with other elements by any mechanism and at any rate.
The three broad types of coprecipitation are inclusion, adsorption, and solid-
solution formation.

Table 1.4

Occurrence of trace elements in primary minerals.

Element Principal modes of occurrence in primary minerals

B Tourmaline, borate minerals; isomorphic substitution for Si in micas

Ti Rutile and ilmenite (FeTiOa); oxide inclusions in silicates

V Isomorphic substitution for Fe in pyroxenes and amphiboles, and for Al in

micas; substitution for Fe in oxides
Cr Chromite (FeC^C^); isomorphic substitution for Fe or Al in other

minerals of the spinel group
Co Isomorphic substitution for Mn in oxides and for Fe in pyroxenes,

amphiboles, and micas
Ni Sulfide inclusions in silicates; isomorphic substitution for Fe in olivines,

pyroxenes, amphiboles, micas, and spinels
Cu Sulfide inclusions in silicates; isomorphic substitution for Fe and Mg in

olivines, pyroxenes, amphiboles, and micas; and for Ca, K, or Na in

feldspars
Zn Sulfide inclusions in silicates; isomorphic substitution for Mg and Fe in

olivines, pyroxenes, and amphiboles; and for Fe or Mn in oxides
As Arsenopyrite (FeAsS) and other arsenate minerals

Se Selenide minerals; isomorphic substitution for S in sulfides; iron selenite

Mo Molybdenite (M0S2); isomorphic substitution for Fe in oxides

Cd Sulfide inclusions and isomorphic substitution for Cu, Zn, Hg, and Pb in

sulfides
Pb Sulfide, phosphate, and carbonate inclusions; isomorphic substitution for

K in feldspars and micas; for Ca in feldspars, pyroxenes, and phosphates;

and for Fe and Mn in oxides

The Chemical Composition of Soils 15

Table 1.5

Trace elements coprecipitated with secondary soil minerals and soil
humus.

Solid Coprecipitated trace elements

Fe and Al oxides B, P, Ti, V, Cr, Mn, Co, Ni, Cu, Zn, Mo, As, Se, Cd, Pb

Mn oxides P, Fe, Co, Ni, Cu, Zn, Mo, As, Se, Cd, Pb

Ca carbonates P, V, Mn, Fe, Co, Cd, Pb

Hikes B, V, Ni, Co, Cr, Cu, Zn, Mo, As, Se, Pb

Smectites B, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Pb

Vermiculites Ti, Mn, Fe

Humus B, Al, V, Cr, Mn, Fe, Ni, Cu, Zn, Se, Cd, Pb

If a solid phase formed by a trace element has a very different atomic
structure from that of the host mineral, then it is likely that the host mineral
and the trace element will occur together only as morphologically distinct
phases. This kind of association is termed inclusion with respect to the trace
element. For example, CuS occurs as an inclusion — a small, separate phase — in
primary silicates (Table 1.4).

If there is only limited structural compatibility between a trace element
and a corresponding major element in a host mineral, then coprecipitation
produces a mixture of the two elements restricted to the host mineral-soil
solution interface. This mechanism is termed adsorption because the mixed
solid phase that forms is restricted to the interfacial region (including the inter-
layer region of layer- type minerals). Well-known examples of adsorption are
the incorporation of metals like Pb and oxyanions like arsenate into secondary
metal oxides (Table 1.5).

Finally, if structural compatibility is high and diffusion of a trace ele-
ment within the host mineral is possible, a major element in the host mineral
can be replaced sparingly but uniformly throughout by the trace element.
This kind of homogeneous coprecipitation is solid-solution formation. It is
enhanced if the size and valence of the substituting element are compara-
ble with those of the element replaced. Examples of solid-solution formation
occur when precipitating secondary aluminosilicates incorporate metals like
Fe to replace Al in their structures (Table 1.5) or when calcium carbonate
precipitates with Cd replacing Ca in the structure. Soil solid phases bearing
trace elements serve as reservoirs, releasing the trace elements slowly into
the soil solution as weathering continues. If a trace element is also a nutri-
ent, then the rate of weathering becomes a critical factor in soil fertility. For
example, the ability of soils to provide Cu to plants depends on the rate at
which this element is transformed from a solid phase to a soluble chemical
form. Similarly, the weathering of soil solids containing Cd as a trace element
will determine the potential hazard of this toxic element to microbes and
plants.

16 The Chemistry of Soils

1.4 Soil Air and Soil Water

The fluid phases in soil constitute between one and two thirds of the soil
volume. The gaseous phase, soil air, typically is the same kind of fluid mixture as
atmospheric air. Because of biological activity in soil, however, the percentage
composition of soil air can differ considerably from that of atmospheric air
(781 mL N 2 , 209 mL 2 , 9.3 mL Ar, and 0.33 mL C0 2 in 1 L dry air). Well-
aerated soil contains 180 to 205 mL 2 L soil air, but this can drop to 100
mL L _1 at 1 m below the soil surface, after inundation by rainfall or irrigation,
or even to 20 mL L _1 in isolated soil microenvironments near plant roots.
Similarly, the fractional volume of C0 2 in soil air is typically 3 to 30 mL L ,but
can approach 100 mL L at a 1-m depth in the vicinity of plant roots, or after
the flooding of soil. This markedly higher C0 2 content of soil air relative to that
of the atmosphere has a significant impact on both soil acidity and carbonate
chemistry. Soil air also contains variable but important contributions from
H 2 , NO, N 2 0, NH3, CH4, and H 2 S produced with microbial mediation under
conditions of low or trace oxygen content.

Soil water is found principally as a condensed fluid phase, although the
content of water vapor in soil air can approach 30 mL L in a wet soil.
Soil water is a repository for dissolved solids and gases, and for this reason
is referred to as the soil solution. With respect to dissolved solids, those that
dissociate into ions (electrolytes) in the soil solution are most important to the
chemistry of soils. The nine ion-forming chemical elements with concentra-
tions in uncontaminated soil solutions that typically exceed all others are C
(HCO3-), N (NO J), Na (Na+), Mg (Mg 2 +), Si [Si(OH)°], S (SO 2 "), Cl (CI"),
K (K + ), and Ca (Ca + ), where the principal chemical species of the element
appears in parentheses or square brackets. [The neutral species Si(OH);j is
silicic acid.] With the exception of Cl, all are macroelements.

The partitioning of gases between soil air and the soil solution is an
important process contributing to the cycling of chemical elements in the soil
environment. When equilibrium exists between soil air and soil water with
respect to the partitioning of a gaseous species between the two phases, and if
the concentration of the gas in the soil solution is low, the equilibrium can be
described by a form of Henry's law:

K U = [A(aq)]/P A (1.1)

where Ku is a parameter with the units moles per cubic meter per atmosphere
of pressure, known as the Henry's law constant, [A] is the concentration of
gas A in the soil solution (measured in moles per cubic meter), and Pa is
the partial pressure of A in soil air (measured in atmospheres). Table 1.6 lists
values of Kh at 25 °C for 10 gases found in soil air. As an example of the use of
this table, consider a flooded soil in which C0 2 and CH4 are produced under
microbial mediation to achieve partial pressures of 14 and 10 kPa respectively,
as measured in the headspace of serum bottles used to contain the soil during

The Chemical Composition of Soils 17

Table 1.6

The "Henry's law constant" for 10 soil gases at 25°C a .

Gas Ku (mol m~ 3 atm -1 ) Gas Kh (molm~ 3 atm -1 )

H 2

0.78

co 2

34.20

N 2

0.65

CH 4

1.41

o 2

1.27

NH 3

5.71 x 10 4

so 2

1.36 x 10 3

N 2

24.17

H 2 S

1.02 x 10 2

a Based on data compiled from Lide, D. R. (ed.) (2004) CRChandbook
of chemistry and physics, pp. 8-86-8-89. CRC Press, Boca Raton, FL.

incubation. According to Table 1.6, the corresponding concentrations of the
two gases in the soil solution are

[C0 2 (aq)] = 34.03 mol m~ 3 x I 14 kPa x 1 atm J
atm \ 101.325 kPa/

= 4.7 mol m -3

,- / \-i 1-41 molrn" , _,

|CH 4 (aq)| = x 0.0987 atm = 0.14 mol m 3

atm

(The units appearing here are discussed in the Appendix.) The result for CO2 is
noteworthy, in that the concentration of this gas in a soil solution equilibrated
with the ambient atmosphere would be 400 times smaller.

1.5 Soil Mineral Transformations

If soils were not open systems, soil minerals would not weather. It is the
continual input and output of percolating water, biomass, and solar energy
that makes soils change with the passage of time. These changes are perhaps
reflected most dramatically in the development of soil horizons, both in their
morphology and in the mineralogy of the soil clay fraction.

Table 1.7 is a broad summary of the changes in clay fraction mineralogy
observed during the course of soil profile development. These changes are
known collectively as the Jackson-Sherman weathering stages.

Early-stage weathering is recognized through the importance of sulfates,
carbonates, and primary silicates, other than quartz and muscovite, in the soil
clay fraction. These minerals survive only if soils remain very dry, or very
cold, or very wet, most of the time — that is, if they lack significant through-
puts of water, air, biota, and thermal energy that characterize open systems
in nature. Soils in the early stage of weathering include Aridisols, Entisols,
and Gelisols at the Order level in the U.S. Soil Taxonomy. Intermediate-stage

18 The Chemistry of Soils

Table 1.7

Jackson-Sherman soil weathering stages.

Characteristic minerals in Characteristic soil chemical Characteristic soil
soil clay fraction and physical conditions properties 3

Early stage

Gypsum

Carbonates

Olivine/pyroxene/

amphibole

Fe(II)-bearing

micas

Feldspars

Intermediate stage

Quartz

Dioctahedral

mica/illite

Dioctahedral ver-

miculite/chlo rite

Smectite

Advanced stage
Kaolinite
Gibbsite
Iron oxides
Titanium oxides

Low water and
humus content,
very limited
leaching
Reducing

environments, cold
environments
Limited amount of
time for
weathering

Retention of Na, K,
Ca, Mg, Fe(II), and
silica; moderate
leaching, alkalinity
Parent material
rich in Ca, Mg, and
Fe(II),butnot
Fe(II) oxides
Silicates easily
weathered

Removal of Na, K,
Ca,Mg,Fe(II),and
silica

Intensive leaching
by fresh water
Oxidation of Fe(II)
Low pH and
humus content

Minimally
weathered soils:
arid or very cold
regions,
waterlogging,
recent deposition

Soils in temperate
regions: forest or
grass cover,
well-developed A
and B horizons,
accumulation of
humus and clay
minerals

Soils under forest
cover with high
temperature and
precipitation:
accumulation of
Fe(III) and Al
oxides, absence of
alkaline earth
metals

a Soil taxa corresponding to these properties are discussed in Encyclopedia Britannica
(2005) Soil. Available at www.britannica.com/eb/.

weathering features quartz, muscovite, and layer-type secondary aluminosili-
cates (clay minerals) prominently in the clay fraction. These minerals survive
under leaching conditions that do not entirely deplete silica and the major
elements, and do not result in the complete oxidation of ferrous iron [Fe(II)],
which is incorporated into illite and smectite. Soils at this weathering stage
include the Mollisols, Alfisols, and Spodosols. Advanced-stage weathering, on

The Chemical Composition of Soils 19

the other hand, is associated with intensive leaching and strongly oxidizing
conditions, such that only hydrous oxides of aluminum, ferric iron [Fe(III)],
and titanium persist ultimately. Kaolinite will be an important clay mineral if
the removal of silica by leaching is not complete, or if there is an invasion of
silica-rich waters, as can occur, for example, when siliceous leachate from the
upper part of a soil toposequence moves laterally into the profile of a lower
part. The Ultisols and Oxisols are representative soil taxa.

The order of increasing persistence of the soil minerals listed in Table 1.7
is downward, both among and within the three stages of weathering. The
primary minerals, therefore, tend to occur higher in the list than the secondary
minerals, and the former can be linked with the latter by a variety of chemical
reactions. Of these reactions, the most important is termed hydrolysis and
protonation, which may be illustrated by the weathering of the feldspar albite
or the mica biotite, to form the clay mineral kaolinite (Table 1.3). For albite
the reaction is

4 NaAlSi 3 8 (s) + 4H+ + 18 H 2 (£) = Si 4 Al 4 Oio(OH)8 (s)
(albite) (kaolinite)

+ 8 Si(OH)!| + 4Na+ (1.2)

where solid (s) and liquid (I) species are indicated explicitly, all undesignated
species being dissolved solutes by default. The corresponding reaction for
biotite is

2K2[Si 6 Al2]Mg 3 Fe(II)3 2 o(OH) 4 (5) + 16 H+

+ 11H 2 0(£) + ^0 2 (g)

= Si 4 Al 4 Oio(OH) 8 (s) + 6 FeOOH (s) + 8 Si(OH)^
(kaolinite) (goethite)

+ 4K++6Mg 2+ (1.3)

in which the iron oxyhydroxide, goethite, is also formed. In both reactions,
which are taken conventionally to proceed from left to right, the dissolution
of a primary silicate occurs through chemical reaction with water and protons
to form one or more solid-phase products plus dissolved species, which are
then subject to leaching out of the soil profile. These two reactions illustrate
an incongruent dissolution, as opposed to congruent dissolution, in which only
dissolved species are products. The basic chemical principles underlying the
development of eqs. 1.2 and 1.3 are discussed in Special Topic 1, at the end of
this chapter.

The incongruent dissolution of biotite, which contains only ferrous iron
[Fe(II)], to form goethite, which contains only ferric iron [Fe(III)], illustrates
the electron transfer reaction termed oxidation (in the case of Eq. 1.3, the

20 The Chemistry of Soils

oxidation of ferrous iron) — an important process in soil weathering. (Oxi-
dation, the loss of electrons from a chemical species, is discussed in Chapter
6.) Another important weathering reaction is complexation, which is the reac-
tion of an anion (or other ligand) with a metal cation to form a species that
can be either dissolved or solid phase. In the case of albite weathering by
complexation,

NaAlSi 3 8 (s) +4H+ + CzO^" + 4 H 2 (£)
(albite)

= A1C 2 0+ + 3 Si(OH)° + Na+ (1.4)

The organic ligand on the left side of Eq. 1.4, oxalate, is the anion formed by
complete dissociation of oxalic acid (H2C2O4, ethanedioic acid) at pH > 4.2.
It complexes Al 3+ released by the hydrolysis and protonation of albite. The
resulting product is shown on the right side of Eq. 1.4 as a soluble complex
that prevents the precipitation of kaolinite (i.e., the dissolution process is
now congruent). Oxalate is a very common anion in soil solutions associated
with the life cycles of microbes, especially fungi, and with the rhizosphere, the
local soil environment influenced significantly by plant roots. Organic anions
produced by microbes thus play a significant role in the weathering of soil
minerals, particularly near plant roots, where anion concentrations can be in
the moles per cubic meter range.

The three weathering reactions surveyed very briefly in this section pro-
vide a chemical basis for the transformation of soil minerals among the
Jackson— Sherman weathering stages. With respect to silicates, a master vari-
able controlling these transformations is the concentration of silicic acid in
the soil solution. As the concentration of Si(OH)° decreases through leaching,
the mineralogy of the soil clay fraction passes from the primary minerals of the
early stage to the secondary minerals of the intermediate and advanced stages.
Should the Si(OH)^ concentration increase through an influx of silica, on the
other hand, the clay mineralogy can shift upward in Table 1.7. This possible
behavior is in fact implied by the equal-to sign in the chemical reactions in
eqs. 1.2 through 1.4.

For Further Reading

Churchman, G. J. (2000) The alteration and formation of soil minerals by
weathering, pp. F-3-F-76. In: M.E. Sumner (ed.), Handbook of soil science.
CRC Press, Boca Raton, FL. A detailed, field-oriented discussion of the
chemical weathering processes that transform primary minerals in soils.

Dixon, J. B., and D. G. Schulze (eds.). (2002) Soil mineralogy with environmen-
tal applications. Soil Science Society of America, Madison, WI. A standard
reference work on soil mineral structures and chemistry.

The Chemical Composition of Soils 21

Frausto da Silva, J. J. R., and R. J. P. Williams. (2001) The biological chemistry
of the elements. Oxford University Press, Oxford. An engaging discussion
of the bioinorganic chemistry of the elements essential to (or inimical to)
life processes at the cellular level.

Gregory, P. J. (2006) Roots, rhizosphere and the soil: The route to a better
understanding of soil science? Eur. J. Soil Sci. 57:2-12. A useful historical
introduction to the concept of the rhizosphere and its importance to
understanding the plant— soil interface.

Kabata-Pendias, A., and H. Pendias. (2001) Trace elements in soils and plants.
CRC Press, Boca Raton, FL. A compendium of analytical data on trace
elements in the lithosphere and biosphere, organized according to the
Periodic Table.

Stevenson, F. J., and M. A. Cole. (1999) Cycles of soil. Wiley, New York. An
in-depth discussion of the biogeochemical cycles of C, N, P, S, and some
trace elements, addressed to the interests of soil chemists.

Problems

The more difficult problems are indicated by an asterisk.

1. The table presented here lists area-normalized average soil C content
and annual soil C input, along with mean annual precipitation (MAP),
for biomes grouped by mean annual temperature (MAT). Analyze this

Soil C content 3

C input rate

MAP

Biome

(mt ha~ 1 )

(mt ha" 1 y~ 1 )

(mm)

MAT = 5° C

Boreal desert

102

0.5

125

Boreal forest (moist)

116

1.9

375

Boreal forest (wet)

193

6.8

1250

MAT = 9° C

Cool desert

2.1

125

Cool grassland

133

3.0

375

Cool temperate forest

127

9.1

2250

MAT = 24° C

Warm desert

0.4

125

Tropical grassland

4.8

375

Tropical forest (dry)

4.6

1250

Tropical forest (moist)

114

24.9

2500

Tropical forest (wet)

191

37.3

6000

a mt = metric ton = 10 3 kg; ha = hectare = 10 4 m 2

22 The Chemistry of Soils

information quantitatively (e.g., perform statistical regression analyses)
to discuss correlations between soil C content and the climatic variables
MAP and MAT.

2. The average residence time of an element in a storage component of its
biogeochemical cycle is the ratio of the mass of the element in the storage
component to the rate of element output from the component, calcu-
lated under the assumption that the rates of output and input are equal
(steady-state condition). Calculate the residence times of C in soil humus
for the biomes listed in the table in Problem 1. These residence times may
be attributed primarily to soil C loss by emission (Fig. 1.1) as CO2 (soil
respiration), if a steady state obtains. Discuss correlations between the C
residence times and the two climate variables MAT and MAP.

*3. The average age of soil humus determined by g 4 C dating typically ranges
from centuries to millennia, which is significantly longer than the res-
idence times of soil C calculated in Problem 2 using the data in the
table given with Problem 1. This paradox suggests that soil C has at least
two components with widely different turnover rates. Detailed studies of
humus degradation at field sites in boreal, temperate, and tropical forests
indicated soil C residence times of 220, 12, and 3 years respectively for
the three field sites, whereas Jc dating yielded soil humus ages of 950,
250, and 1050 years respectively. Measurements of the fraction of soil C
attributable to humic substances gave 62%, 78%, and 22% respectively.
Use these data to estimate the average age of humic substances in the three
soils. (Hint: The inverse of the soil C residence time equals the weighted
average of the inverses of the two component residence times, whereas
the average age of soil C is equal to the weighted average of the ages of the
two components. In each case, the weighting factors are the fractions of
soil C attributable to the two components. To a good first approximation,
the "old" component can be neglected in the first expression, whereas
the "young" component can be neglected in the second one. Check this
approximation assuming that residence time and Jc age are the same for
each humus component.)

4. Consult a suitable reference to prepare a list of metals that are essential
to the growth of higher plants. Use Table 1.2 to classify these metals into
groups of major and trace elements in soils. Use Table 2.1 to calculate the
IPs of the metals in their most common valence states, then examine your
results for relationships between IP and (a) mean soil content, (b) AMF,
and (c) toxicity classification (Fig. 1.3).

5. The table presented here lists the average content of organic C and
five metals in agricultural soils of the United States, grouped accord-
ing to the Order level in U.S. Soil Taxonomy. Compare these data with
those in tables 1.1 and 1.2, and examine them for any relationships

The Chemical Composition of Soils 23

between metal content and Jackson-Sherman weathering stage. Clas-
sify the metals (as bivalent cations) according to their possible toxicity
(Fig. 1.3).

Cd Cu Ni Pb Zn C

Order (mg kg~ 1 ) (mg kg~ 1 ) (mg kg~ 1 ) (mg kg~ 1 ) (mg kg~ 1 ) (g kg~ 1 )

Alfisol

0.112

10.9

12.6

9.6

31.3

8.6

Aridisol

0.304

25.0

24.3

10.6

70.1

6.3

Entisol

0.246

21.1

21.0

10.0

65.5

6.8

Mollisol

0.227

19.1

22.8

10.7

54.4

13.9

Spodosol

0.200

48.3

22.0

10.0

44.1

17.3

Ultisol

0.049

6.2

7.4

8.0

13.8

7.8

6. Careful study of the rhizosphere in a Spodosol under balsam fir and
black spruce forest cover showed that rhizosphere pH was somewhat
lower (pH 4.8 vs. 5.0), whereas organic C was higher (21 g C kg
vs. 5 g C kg -1 ) than in the bulk soil. The table presented here shows
the content of four metals in the rhizosphere (R) and bulk (B) soil
that could be extracted by BaCi2 ("soluble and weakly adsorbed"),
Na4?207 (sodium pyrophosphate, "organic complexes"), and NH5C2O4
(ammonium oxalate, "coprecipitated in a poorly crystalline solid
phase").

a. Explain the differences between major elements and trace
elements with respect to trends across the three extractable
fractions, irrespective of R and B.

b. What is the principal chemical factor determining the differences
between rhizosphere and bulk soil with respect to "weakly
adsorbed" metal? (Hint: Compare the average ratio of weakly
adsorbed metal with C content between R and B.)

Metal

Soil

BaCI 2

Pyrophosphate

Oxalate

AKgkg- 1 )

0.16

5.5

16.1

0.06

4.7

15.4

Fe(gkg- 1 )

0.02

2.0

10.2

0.01

1.5

9.3

Cu (mg kg~

4.0

4.7

9.0

1.7

0.9

4.8

Zn (mg kg~

X )

2.0

4.3

5.5

0.4

1.4

3.9

B, bulk; R, rhizosphere.

24 The Chemistry of Soils

7. Calculate the average chemical formula and its range of variability for soil
humic and fulvic acids using the composition data in the table presented
here. Does the H-to-C molar ratio differ significantly between the two
humic substances?

C H N S O

Humic substance (g kg~ 1 ) (g kg~ 1 ) (g kg~ 1 ) (g kg~ 1 ) (g kg~ 1 )

Humic acid

554 ± 38

48 ± 10

36 ± 13

8±6

360 ±37

Fulvic acid

453 ± 54

50 ± 10

26 ± 13

13 ± 11

462 ± 52

8. Calculate the corresponding concentrations of CO2 dissolved in soil water
as the CO2 partial pressure in soil air increases in the order 3.02 x 10
(atmospheric C0 2 ), 0.003, 0.01, 0.05, 0.10 atm (flooded soil).

9. The ideal gas law, PV = nRT, can be applied to the constituents of soil
air to a good approximation, where P is pressure, V is volume, n is the
number of moles, _R is the molar gas constant, and T is absolute temper-
ature, as described in the Appendix. Use the ideal gas law to show that Eq.
1.1 can be rewritten in the useful form

H = [A(g)]/[A(aq)]

where [ ] is a concentration in moles per cubic meter, and H = 10 /K^RT
is a dimensionless constant based on R = 0.08206 atm L mol K , and
T in Kelvin (K). Prepare a table of H values based on Table 1.6.

10. The table presented here shows partial pressures of O2 and N2O in the
pore space of an Alfisol under deciduous forest cover as a function of
depth in the soil profile. Calculate the N20-to-02 molar ratio in soil air
and in the soil solution as a function of depth.

Depth (m) P 2(atm) P N2 o (10~ 6 atm)

0.1
0.2
0.4
0.6

11. Write a balanced chemical reaction for the congruent dissolution of the
olivine forsterite (Mg2Si04) by hydrolysis and protonation.

0.14

2.3

0.13

3.5

0.10

7.7

0.09

20.8

The Chemical Composition of Soils 25

12. Feldspar can weather to form gibbsite instead of kaolinite. Write a bal-
anced chemical reaction for the incongruent dissolution of K-feldspar
(KAlSi3 0g) to produce gibbsite by hydrolysis and protonation.

*13. Write a balanced chemical reaction for the incongruent dissolution
of the mica muscovite, [K2[Si6Al2]Al402o(OH)4], to form the smec-
tite, Kio8[Si6.92Ali.o8]Al402o(OH)4, by hydrolysis and protonation. This
smectite is an example of the common soil clay mineral beidellite.

14. Each formula unit of soil fulvic acid can dissociate about 40 protons at
circumneutral pH to become a negatively charged polyanion. With respect
to its soil solution chemistry as a complexing ligand, fulvic acid thus can be
represented simply by the formula H40L, where L 40_ denotes the chemical
formula of the highly charged polyanion (fulvate) that remains after 40
protons are deleted from the chemical formula given in Section 1.3. Use
this convention to write a balanced chemical reaction for the congruent
dissolution of albite by complexation, hydrolysis, and protonation, with
a neutral complex between hydrolyzed Al + (i.e., AlOH + ) and fulvate as
one of the products.

15. When CO2 dissolves in the soil solution, it solvates to form the chemical
species CO2 -H^O and the neutral complex H2CO3 (a very minor species),
which together are denoted H2CO* (carbonic acid). Carbonic acid, in
turn, dissociates a proton to leave the species HCO^~ (bicarbonate ion).
Write a series of balanced chemical reactions that show the formation of
H2COI from C02(g), the formation of bicarbonate from carbonic acid,
and the reaction of bicarbonate with Ca-feldspar (CaSi2Al20s) to form
calcite and kaolinite. Sum the reactions to develop an overall reaction for
the weathering of Ca-feldspar by reaction with C02(g).

Special Topic 1: Balancing Chemical Reactions

Chemical reactions like those in eqs. 1.2 through 1.4 must fulfill two general
conditions: mass balance and charge balance. Mass balance requires that the
number of moles of each chemical element be the same on both sides of the
reaction when written as a chemical equation. Charge balance requires that
the net total ionic charge be the same on both sides of the reaction. These
constraints can be applied to develop the correct form of a chemical reaction
when only the principal product and reactant are given.

As a first example, consider the incongruent dissolution of albite,
NaAlSiaOg, to produce kaolinite, Si4Al40io(OH)s, as in Eq. 1.2. Because 1
mol of reactant albite contains 1 mol Na, 1 mol Al, and 3 mol Si, whereas 1
mol of product kaolinite contains 4 mol Si and Al, these amounts, by mass

26 The Chemistry of Soils

balance, must appear equally on both sides of the reaction:

4NaAlSi 3 8 (s) — > Si 4 Al 4 Oio(OH)8(s) + 8Si(OH)2 + 4Na+ (S.l.l)

where the excess Si has been put into silicic acid, the dominant aqueous species
of Si(IV) at pH less than 9. A mechanism for the reaction, hydrolysis and
protonation, is then invoked:

4NaAlSi 3 8 (s) + H++ H 2 0(£) — > Si 4 Al 4 O 10 (OH) 8 (s)

+ 8Si(OH) 4 l + 4Na+ (S.1.2)

Charge balance requires adding 3 mol protons to the left side to match the
four cationic charges on the right side:

4NaAlSi 3 8 (s) + 4H++ H 2 0(£) — > Si 4 Al 4 Oi (OH) 8 (s)

+ 8Si(OH)° + 4Na+ (S.1.3)

Mass balance for protons now is considered. There are 40 mol H on the
right side (8 mol from kaolinite and 4x8 = 32 mol from silicic acid), but only
6 mol on the left side, so 34 mol H are needed. This need is met by changing
the stoichiometric coefficient of water to 18:

4NaAlSi 3 8 (s) +4H++ 18H 2 0(£) = Si 4 Al 4 Oi (OH) 8 (s)

+ 8Si(OH)° + 4Na+ (S.1.4)

Note that 50 mol O now appears on both sides of the reaction to give O
mass balance.

The same procedure is used to develop the more complex reaction in
Eq. 1.3:

2 K 2 [Si 6 Al 2 ]Mg 3 Fe(II) 3 O 20 (OH) 4 (s) — ►

Si 4 Al 4 Oio(OH) 8 (s) + 6FeOOH(s) + 8Si(OH)° + 4K+ + 6Mg 2+

(S.1.5)

bearing in mind that the products have been selected to be kaolin-
ite and goethite. In this example, there are two mechanisms invoked —
hydrolysis/protonation and oxidation:

2K 2 [Si 6 Al 2 ]Mg 3 Fe(II) 3 O 20 (OH) 4 (s) + H+ + H 2 0(£) + 2 (g) — ►

Si 4 Al 4 Oio(OH) 8 (s) + 6FeOOH(s) + 8Si(OH)^ + 4K+ + 6Mg 2+

(S.1.6)

The next step is charge balance. The net ionic charge on the right side of
Eq. S.1.6 is 16 cationic charges (6 from Mg, 4 from K, and 6 from Fe), thus

The Chemical Composition of Soils 27

requiring 16 as the stoichiometric coefficient of H + on the left side:

2K 2 [Si 6 Al 2 ]Mg 3 Fe(II)302o(OH)4(s) + 16H+ + H 2 0(£) + 2 (g)
— > Si 4 Al 4 Oio(OH)8(s) + 6FeOOH(s) + 8Si(OH)!j
+ 4K+ + 6Mg 2+ (S.1.7)

Mass balance on H in Eq. S.1.7 requires the addition of 20 mol H on the
left side (2x4+16 + 2 = 26 vs. 8 + 6 + 8x4 = 46), which is accomplished
by changing the stoichiometric coefficient of water to 1 1:

2K 2 [Si 6 Al 2 ]Mg 3 Fe(II)30 2 o(OH) 4 (s) + 16H+ + 11 H 2 0(£) + 2 (g)
— > Si 4 Al 4 Oio(OH) 8 (s) + 6FeOOH(s) + 8 Si(OH)^
+ 4K+ + 6Mg 2+ (S.1.8)

Finally, unlike the case of Eq. S.1.4, mass balance on O is not satisfied
unless 1 molO is added to the left side of Eq. S.1.8 (2 x24 + 11 + 2 = 61 vs.
18 + 6x2 + 8x4 = 62):

2K 2 [Si 6 Al 2 ]Mg 3 Fe(II) 3 2 o(OH) 4 (s) + 16 H+

+ 11H 2 0(£) + ^0 2 (g)

= Si 4 Al 4 Oio(OH) 8 (s) + 6FeOOH(s) + 8Si(OH)°

+ 4K+ + 6Mg 2+ (S.1.9)

Note that in both of these examples, reactants and products, as well as the
mechanisms of reaction, are free choices to be made before imposing the mass
and charge balance constraints.

Soil Minerals

2.1 Ionic Solids

The chemical elements making up soil minerals occur typically as ionic species
with an electron configuration that is unique and stable regardless of whatever
other ions may occur in a mineral structure. The attractive interaction between
one ion and another of opposite charge nonetheless is strong enough to form a
chemical bond, termed an ionic bond. Ionic bonds differ from covalent bonds,
which involve a significant distortion of the electron configurations (orbitals)
of the bonding atoms that results in the sharing of electrons. Electron sharing
mixes the electronic orbitals of the atoms, so it is not possible to assign to each
atom a unique configuration that is the same regardless of the partner with
which the covalent bond has formed. This loss of electronic identity leads to a
more coherent fusion of the orbitals that makes covalent bonds stronger than
ionic bonds.

Ionic and covalent bonds are conceptual idealizations that real chemical
bonds only approximate. In general, a chemical bond shows some degree of
ionic character and some degree of electron sharing. The Si-O bond, for exam-
ple, is said to be an even partition between ionic and covalent character, and the
Al-O bond is thought to be about 40% covalent, 60% ionic. Aluminum, how-
ever, is exceptional in this respect, for almost all the metal-oxygen bonds that
occur in soil minerals are strongly ionic. For example, Mg-O and Ca-O bonds
are considered 75% to 80% ionic, whereas Na-O and K-O bonds are 80%
to 85% ionic. Covalence thus plays a relatively minor role in determining the
atomic structure of most soil minerals, aside from the important feature that

Soil Minerals 29

Si-O bonds, being 50% covalent, impart particular stability against mineral
weathering, as discussed in Section 1.3.

Given this perspective on the chemical bonds in minerals, the two most
useful atomic properties of the ions constituting soil minerals should be their
valence and radius. Ionic valence is simply the ratio of the electric charge
on an ionic species to the charge on the proton. Ionic radius, however, is
a less direct concept, because the radius of a single ion in a solid cannot
be measured. Ionic radius thus is a defined quantity based on the following
three assumptions: (1) the radius of the bivalent oxygen ion (O ) in all
minerals is 0.140 nm, (2) the sum of cation and anion radii equals the measured
interatomic distance between the two ions, and (3 ) the ionic radius may depend
on the coordination number, but otherwise is independent of the type of
mineral structure containing the ion. The coordination number is the number
of ions that are nearest neighbors of a given ion in a mineral structure. Table 2.1
lists standard cation radii calculated from crystallographic data under these
three assumptions. Note that the radii depend on the valence (Z) as well as the
coordination number (CN) of the metal cation. The radius decreases as the
valence increases and electrons are drawn toward the nucleus, but it increases
with increasing coordination number for a given valence. The coordination
numbers found for cations in soil minerals are typically 4 or 6, and occasionally
8 or 12. The geometric arrangements of anions that coordination numbers
represent are illustrated in Figure 2.1. Each of these arrangements corresponds
to a regular geometric solid (a polyhedron, as shown in the middle row of
Fig. 2.1). It is evident that the strength of the anionic electrostatic field acting
on a cation will increase as its coordination number increases. This stronger
anionic field draws the "electron cloud" of the cation more into the void space
between the anions, thereby causing the cation radius to increase with its
coordination number.

Two important physical parameters can be defined using the atomic
properties listed in Table 2.1. The first parameter is ionic potential (or IP),

Z
IP=— (2.1)

which is proportional to the coulomb potential energy at the periphery of a
cation, as discussed in Section 1.2. The second parameter is bond strength (s),
a more subtle concept from Linus Pauling,

s=^ (2.2)

which is proportional to the electrostatic flux emanating from (or converging
toward) an ion along one of the bonds it forms with its nearest neighbors.
Given that the number of these latter bonds equals CN, it follows that the
sum of all bond strengths assigned to an ion in a mineral structure is equal to
the absolute value of its valence (i.e., |Z|). This characteristic property of bond
strength is a special case of Gauss' law in electrostatics.

30 The Chemistry of Soils

TETRAHEDRAL OCTAHEDRAL

CUBIC

CU BO-
OCTAHEDRAL

4 6 8 12

Figure 2.1. The principal coordination numbers for metal cations in soil minerals,
illustrated by closely packed anion spheres (top), polyhedra enclosing a metal cation
(middle), and "ball-and- stick" drawings (bottom).

The chemical significance of bond strength can be illustrated
by an application to the four oxyanions discussed in Section i.f:
NO^~,S0 4 _ , C0 3 ~, and P0 4 ~. The strength of the bond between the cen-
tral cation and one of the peripheral O in each of the four oxyanions can be
calculated using Eq. 2.2:

1.67 vu (NO")

1.33 vu (CO3 )

1.50 vu (S0 4 )

1.25 vu (PO^ )

where vu means valence unit, a conventional (dimensionless) unit for bond
strength. Note that the sum of the bond strengths assigned to each central
cation is equal to its valence (e.g., 3 x 5/3 = 5, the valence of N in the nitrate
anion). But, because none of these bond strengths equals 2.0 (the absolute
value of the valence of O 2- ), any peripheral oxygen ion still has the ability to
attract and bind an additional cationic charge external to the oxyanion. This
conclusion follows specifically from Gauss' law, mentioned earlier, although it
is also evident from the overall negative charge on each oxyanion. It is apparent
that the strength of an additional bond formed between a peripheral oxygen
ion and any external cationic charge will be smallest for nitrate (i.e., 2.00
- 1.67 = 0.33 vu) and largest for phosphate (i.e., 0.75 vu), with the resultant
ordering: NO^~ < S0 4 ~ < C0 3 ~ < P0 4 ~. This ordering is also the same
as observed experimentally for the reactivity of these anions with positively

Soil Minerals 31

Table 2.1

Ionic radius (IR), coordination number (C/V), and valence (Z) of metal and
metalloid cations. 3

Metal Z CN IR (nm) Metal Z CN IR (nm)

0.059

0.075

0.076

0.061

0.102

0.069

0.072

0.057

0.039

0.073

0.054

0.074

0.026

0.058

0.138

0.034

0.151

0.118

0.164

0.084

0.100

0.041

0.112

0.115

0.061

0.095

0.062

0.167

0.026

0.188

0.083

0.135

0.065

0.119

0.053

0.102

0.078

0.119

0.065

0.078

a Shannon, R. D. (1976) Revised effective ionic radii and systematic studies of interatomic distances
in halides and chalcogenides. Acta. Cryst A32:75 1-767.

charged sites on particle surfaces (noted in Section 1.1), and it is the order of
increasing affinity of the anions for protons in aqueous solution, as indicated
by the pH value at which they will bind a single proton. The example given
here shows that bond strength can be pictured as the absolute value of an
effective valence of an ion, assigned to one of its bonds under the constraint
that the sum of all such effective valences must equal the absolute value of the
actual valence of the ion.

Bond strength usually has only one or two values for cations of the
Class A metals discussed in Section 1.2, because these metals typically exhibit
only one or two preferred coordination numbers in mineral structures, but
bond strength can be quite variable for cations of Class B metals. This hap-
pens because of their large polarizability (i.e., large deformability of their
electron clouds), which allows them access to a broader range of coordina-
tion numbers. A prototypical example is the Class B metal cation Pb , for
which coordination numbers with O ranging from 3 to 12 are observed,
with the corresponding bond strengths then varying from 0.67 to 0.17 vu,
according to Eq. 2.2. This kind of broad variability and the tendency of cation

32 The Chemistry of Soils

radii to increase with coordination number, as noted earlier, suggest that an
inverse relationship should exist between the ionic radius of Pb + and its bond
strength (an idea also from Linus Pauling). Systematic analyses of thousands
of mineral structures have shown that the exponential formula

s = exp [27.03 (R - R)] (2.3)

provides an accurate mathematical representation of how bond strength s
decreases with increasing length of a bond (R, in nanometers) between a
metal cation and an oxygen ion. Values of the parameter, Ro, the metal cation-
oxygen ion bond length that, for a given cation valence, would yield a bond
strength equal to 1.0 vu, are listed in Table 2.2 for the metal and metalloid
cations in Table 2.1. If the bond strength of Pb + ranges from 0.67 to 0.17 vu,
one finds with Eq. 2.3 and Ro = 0.2112 nm, introduced from Table 2.1, that
the corresponding range of the Pb-O bond length in minerals is from 0.226
to 0.277 nm.

Seen the other way around, as a means for calculating bond strength from
a measured value of R, Eq. 2 .3 provides an alternative to Eq. 2 .2 . As an example,

Table 2.2

Bond valence parameter R (Eq. 2.3) for metals and metalloids coordinated to
oxygen. 3

Metal Z R (nm) Metal Z R (nm)

0.1466

0.1654

0.1803

0.1679

0.1693

0.1704

0.1651

0.1789

0.1624

0.1767

0.2132

0.2118

0.1967

0.1928

0.1815

0.1907

0.1724

0.1842

0.1794

0.1904

0.1790

0.2417

0.1760

0.2285

0.1753

0.1972

0.1734

0.2112

0.1759

0.2042

2
3

0.1692
0.1634

a Brown, I. D., and D. Alternatt. (1985) Bond-valence parameters obtained from a systematic
analysis of the inorganic crystal structure database. Acta. Cryst. B41:244.
The average standard deviation of Ro in this table is 0.0042 nm.

Soil Minerals 33

consider Al , for which Eq. 2.3 takes on the form

s = exp [27.03(0.1651 - R)] (2.4)

where R is now the length of an Al— O bond in nanometers. In the aluminum
oxide mineral corundum (AI2O3), Al 3+ is in octahedral coordination with
O 2- . Two different Al-O bond lengths are actually observed in this mineral
(0.185 nm and 0.197 nm), corresponding to s values of 0.584 and 0.422 vu
respectively. These two bond strengths bracket the ideal value of 0.50 calcu-
lated with Eq. 2.2 using Z = 3, CN = 6. When bond strength is calculated
with Eq. 2.3 instead of Eq. 2.2, it is termed bond valence, not only to avoid con-
fusion with the original Pauling definition, but also to emphasize its chemical
interpretation as an effective valence of the ion to which it is assigned.

The electrostatic picture of ionic solids also has significant implications
for what kinds of atomic structures these solids can have. The structures of
most of the minerals in soils can be rationalized on the physical grounds that
the atomic configuration observed is that which tends to minimize the total
electrostatic energy. This concept has been formulated in a most useful fashion
through a set of descriptive statements known as the Pauling Rules:

Rule 1: A polyhedron of anions is formed about each cation. The

cation-anion distance is determined by the sum of the respective
radii, and the coordination number is determined by the radius
ratio of cation to anion.

Minimum radius ratio Coordination number

1.00 12

0.732 8

0.414 6

0.225 4

Rule 2: In a stable crystal structure, the sum of the strengths of the bonds
that reach an anion from adjacent cations is equal to the absolute
value of the anion valence.

Rule 3: The cations maintain as large a separation as possible from one

another and have anions interspersed between them to screen their
charges. In geometric terms, this means that polyhedra tend not to
share edges or especially faces. If edges are shared, they are
shortened relative to the unshared edges.

Rule 4: In a structure comprising different kinds of cation, those of high
valence and small coordination number tend not to share
polyhedron elements with one another.

Rule 5: The number of essentially different kinds of ion in a crystal

structure tends to be as small as possible. Thus, the number of

34 The Chemistry of Soils

different types of coordination polyhedra in a closely packed array
of anions tends to be a minimum.

Pauling Rule 1 is a statement that has the same physical meaning as
Figure 2.1. The anion polyhedra mentioned in the rule are shown in the
middle of the figure, and the bottom row of "ball-and-stick" cartoons shows
the cation-anion bonds with lengths that are determined by the ionic radii.
The radius of the smallest sphere that can reside in the central void created
by closely packing anions in the four ways shown at the top of the figure
can be calculated with the methods of Euclidean geometry. It turns out that
this radius is always proportional to the radius of the coordinating anion. For
example, in the case of tetrahedral coordination, the smallest cation sphere
that can fit inside the four coordinating anions has a radius that is 22.5% of
the anion radius, and for six coordinating anions, it is 41.4% of the anion
radius. These minimum cation radii are listed as decimal fractions in the table
that accompanies Pauling Rule 1. Specific examples of the cation-to-oxygen
radius ratio can be calculated with the IR data in Table 2.1 and the defined O
radius of 0.140 nm. Any cation with a coordination number of 6, for example,
should have an ionic radius > 0.058 nm (=0.414 x 1.40). This is the case for
all but two of the IR values in the table for CN = 6, illustrating the impor-
tant further point that that Pauling Rules are good approximations based on a
strictly electrostatic viewpoint.

Pauling Rule 2 will be recognized as a restatement of Gauss' law in terms
of bond strength defined in Eq. 2.2. For most soil minerals, the anion to
which the rule is applied is O 2- , although OH - , C0 3 ~, and S0 4 ~ also figure
importantly (Table 1.3). As an example, consider the oxygen ions in quartz
(SiC>2), which are coordinated to Si 4+ ions. The radius of Si 4+ is 0.026 nm,
and its usual coordination number is 4. It follows from Eq. 2.2 that 5 = 1.0
for Si 4+ . Because the absolute value of the valence of O 2- is 2, Pauling Rule 2
then permits only two Si 4+ to bond to an O 2- in SiC>2. This means that each
O in quartz must serve as the corner of no more than two silica tetrahedra.
Hypothetical atomic structures for quartz that would involve, say, O at the
corners of three tetrahedra linked together are thus ruled out.

A more subtle example of Pauling Rule 2 occurs in the structure of
the iron oxyhydroxide mineral goethite (FeOOH). The radius of Fe + is
0.065 nm and, by Pauling Rule 1, its coordination number with O must
be 6 (0.065 4- 0.140 = 0.464 > 0.414 => octahedral coordination). Therefore,
s = 0.5 for Fe 3+ , and four Fe 3+ should bond to each O 2- in the goethite
structure, according to Pauling Rule 2. However, inspection of the goethite
structure reveals that each O 2- is bonded to three Fe 3+ , not four (Fig. 2.2).
The proton in the goethite structure can be used to provide a cation for
a fourth bond to O , but because there are twice as many O as H in
goethite, each proton must be shared between two O to satisfy Pauling
Rule 2. If this is the case, then each proton will be doubly coordinated
with O 2- , and its corresponding bond strength will be s = l fe = 0.5,

Soil Minerals 35

OH" Fe 3+ 2+
I 1 I

Goethite

Figure 2.2. "Ball-and-stick" drawing showing the atomic structure of goethite. Note
that the coordination number for O and OH~ is equal to three.

as required. This sharing of a proton between two oxygens is termed
hydrogen bonding (Fig. 2.2), by analogy with electron sharing in covalent
bonding.

Hydrogen bonds seldom involve the proton placed symmetrically between
two oxygens, but instead have one H-O bond significantly shorter (and
stronger) than the other. The stronger H— O bond is about 0.095 nm in
length and has a bond valence described mathematically by Eq. 2.3, with
R = 0.0882 nm, thus yielding s = 0.83 vu. By Gauss' law, the strength of the
weaker bond must be 0.17 vu, because Z = 1 for the proton. Corresponding
to these deviations from the ideal value, s = 0.5 vu, expected for a proton
situated at the midpoint between two oxygens that share it, are those of the
Fe 3+ bond valences in goethite, which actually range from 0.377 to 0.600 vu
because the Fe-O bond lengths vary from 0.212 to 0.195 nm [Eq. 2.3 with
R = 0.1759 nm (Table 2.2)]. Pauling Rule 2 can be satisfied either by three
long Fe-O bonds combined with the stronger H-O bond or by three short
Fe— O bonds combined with the weaker H-O bond.

Pauling Rule 3 reflects coulomb repulsion between cations. The repulsive
electrostatic interaction between the cations in a crystal is weakened effectively,
or screened, by the negatively charged anions in the coordination polyhedra of
the cations. If the cations have a large valence, as does, for example, Si 4+ , then
the polyhedra can do no more than share corners if the cations are to be kept
as far apart as possible in a structural arrangement that achieves the lowest
possible total electrostatic energy. An example of a sheet of silica tetrahedra
sharing corners is shown in Figure 2.3. If the cation valence is somewhat
smaller, as it is for Al , the sharing of polyhedron edges becomes possible.
Figure 2.3 also shows this kind of sharing for a sheet of octahedra comprising
six anions (e.g., O 2- ) bound to a metal cation (e.g., Al 3+ ). Edge sharing brings

36 The Chemistry of Soils

Tetrahedral Sheet

Octahedral Sheet

ditrigonal
hole

occupied
-- octahedra
smaller than
unoccupied

shared edges
5\shorter than
unshared

Figure 2.3. (A, B) Sheet structures in soil minerals formed by linking tetrahedra at
corners (A) or octahedra along edges (B). Reprinted with permission from Schulze,
D. G. (2002) An introduction to soil mineralogy, pp. 1-35. In: J. B. Dixon and D. G.
Schulze (eds.), Soil mineralogy with environmental applications. Soil Science Society of
America, Madison, WI.

the cations closer together than does corner sharing, however, so the task of
charge screening by the anions is made more difficult. They respond to this by
approaching one another slightly along the shared edge to enhance screening.
Doing so, they necessarily shorten the edge relative to unshared edges of the
polyhedra (Fig. 2.3), which is why there are short and long Al— O and Fe-O
bonds in oxide minerals such as corundum (AI2O3) and goethite (FeOOH).

Pauling Rules 4 and 5 continue in the spirit of Rule 3. They reflect the fact
that stable ionic crystals containing different kinds of cation cannot tolerate
much sharing of the coordination polyhedra or much variability in the type
of coordination environment. These and the other three Pauling Rules serve
as useful guides to a molecular interpretation of the chemical formulas for soil
minerals.

2.2 Primary Silicates

Primary silicates appear in soils as a result of deposition processes and from the
physical disintegration of parent rock material. They are to be found mainly
in the sand and silt fractions, except for soils at the early to intermediate
stages of the Jackson-Sherman weathering sequence (Table 1.7), wherein they
can survive in the clay fraction as well. The weathering of primary silicates
contributes to the native fertility and electrolyte content of soils. Among the
major decomposition products of these minerals are the soluble metal cation
species Na + , Mg 2+ , K + , Ca 2+ , Mn 2+ , and Fe 2+ in the soil solution. The metal
cations Co , Cu , and Zn + occur as trace elements in primary silicates
(Table 1.4) and thus are also released to the soil solution by weathering. These
free-cation species are readily bioavailable and, except for Na + , are essential to
the nutrition of green plants. The major element cations — Na + , Mg , and
Ca + — provide a principal input to the electrolyte content in soil solutions.

The names and chemical formulas of primary silicate minerals important
to soils are listed in Table 2.3. The fundamental building block in the atomic

Soil Minerals 37

Table 2.3

Names and chemical formulas of primary silicates found in soils.

Name

Chemical formula

Mineral group

Forsterite

Mg 2 Si0 4

Olivine

Fayalite

Fe 2 Si0 4

Olivine

Chrysolite

Mgi. 8 Feo.2Si0 4

Olivine

Enstatite

MgSi0 3

Pyroxene

Orthoferrosilite

FeSiC-3

Pyroxene

Diopside

CaMgSi 2 6

Pyroxene

Tremolite

Ca 2 Mg 5 Si 8 22 (OH) 2

Amphibole

Actinolite

Ca 2 Mg 4 FeSi 8 22 (OH) 2

Amphibole

Hornblende

NaCa 2 Mg 5 Fe 2 AlSi 7 22 (OH)

Amphibole

Muscovite

K 2 [Si 6 Al 2 ]Al 4 2 o(OH) 4

Mica

Biotite

K 2 [Si 6 Al 2 ]Mg4Fe 2 O 20 (OH) 4

Mica

Phlogopite

K 2 [Si 6 Al 2 ]M g6 O 20 (OH) 4

Mica

Orthoclase

KAlSi 3 8

Feldspar

Albite

NaAlSi 3 8

Feldspar

Anorthite

CaAl 2 Si 2 8

Feldspar

Quartz

Si0 2

Silica

structures of these minerals is the silica tetrahedron: Si0 4 - . Silica tetrahedra
can occur as isolated units, in single or double chains linked together by shared
corners (Pauling Rules 2 and 3), in sheets (Fig. 2.3), or in full three-dimensional
frameworks. Each mode of occurrence defines a class of primary silicate, as
summarized in Figure 2.4.

The olivines comprise individual silica tetrahedra in a structure held
together with bivalent metal cations like Mg , Fe , Ca , and Mn + in octa-
hedral coordination. Solid solution (see Section 1.3) of the minerals forsterite
and fayalite (Table 2.3) produces a series of mixtures with specific names,
such as chrysolite, which contains 10 to 30 mol°/o fayalite. As discussed in
Section 1.3, olivines have the smallest Si-to-O molar ratio among the pri-
mary silicates and, therefore, they feature the least amount of covalence in
their chemical bonds. Their weathering in soil is relatively rapid (timescale
of years), beginning along cracks and defects at the crystal surface to form
altered rinds containing oxidized-iron solid phases and smectite (Table 1.3).
More extensive leaching can result in congruent dissolution (see Problem 1 1
in Chapter 1) or can produce kaolinite instead of smectite, the formation of
either of these clay minerals requiring a proximate source of Al, because none
exists in olivine (except possibly as a trace element).

The pyroxenes and amphiboles contain either single or double chains
of silica tetrahedra that form the repeating unit Si20 6 ~ or Si^,^", respec-
tively, with Si-to-O ratios near 0.33 to 0.36 (Fig. 2.4). The amphiboles feature
isomorphic substitution of Al 3+ for Si 4+ (Table 2.3), and both mineral groups
harbor a variety of bivalent metal cations, as well as Na + , in octahedral

38 The Chemistry of Soils

ISOLATED

CHAIN

SiOJ

SiO"

si 4 ofr

SHEET

FRAMEWORK

SiO,

OLIVINES PYROXENES AMPHIBOLES

MICAS

FELDSPARS, QUARTZ

Figure 2.4. Primary silicates classified by the geometric arrangement of their silica
tetrahedra.

coordination with O 2- to link the silica chains together. The weathering of
these silicates is complex, with smectite and kaolinite, alongwith Al and Fe(III)
oxides, being the principal secondary minerals emerging near structural defect
sites where mineral dissolution begins. Hydrolysis and protonation, along
with oxidation of Fe(II), are the main weathering mechanisms of olivines,
pyroxenes, and amphiboles, although complexation (e.g., by oxalate) plays
a dominant role when weathering is governed by microorganisms, such as
bacteria or fungi.

The micas are built up from two sheets of silica tetrahedra
(Si20 5 ~ repeating unit) fused to each planar side of a sheet of metal cation
octahedra (Fig. 2.3). The octahedral sheet typically contains Al, Mg, and Fe
ions coordinated to O 2- and OH - . If the metal cation is trivalent, only two of
the three possible cationic sites in the octahedral sheet can be filled to achieve
charge balance and the sheet is termed dioctahedral. If the metal cation is biva-
lent, all three possible sites are filled and the sheet is trioctahedral. Isomorphic
substitution of Al for Si, Fe(III) for Al, and Fe or Al for Mg occurs typically
in the micas, along with the many trace element substitutions mentioned in
Table 1.4.

Muscovite and biotite are the common soil micas, the former being
dioctahedral and the latter trioctahedral (Table 2.3). In both minerals, Al 3+
substitutes for Si 4+ . The resulting charge deficit is balanced by K + , which
coordinates to 12 oxygen ions in the cavities of two opposing tetrahedral
sheets belonging to a pair of mica layers stacked on top of one another. Thus
the K + links adjacent mica layers together. It is these linking cations that are
removed first as crystallite edges become frayed and, therefore, vulnerable to
penetration by water molecules and competing soil solution cations during
the initial stage of weathering (Fig. 2.5), which is accelerated by rhizosphere
microorganisms that consume K + from the vicinal soil solution and release

Soil Minerals 39

K replaced with Ij

hydrated cations ft ^

- * V?

some Fe oxidized,
cations ejected,
hydroxyls rotate

adjacent interlayer
K held more tightly

b b>

Figure 2.5. Some pathways of the initial stage of weathering of the trioctahedral
mica, biotite. There is a loss of interlayer K + and oxidation of Fe + in the octahedral
sheet, with consequent rotation of structural OH. Reprinted with permission from
Thompson, M. L., and L. Ukrainczyk. (2002) Micas, pp. 431-466. In: J. B. Dixon
and D. G. Schulze (eds.), Soil mineralogy with environmental applications. Soil Science
Society of America, Madison, WI.

organic acids that complex and dislodge Al exposed at crystallite edges. Ferrous
iron in biotite is gradually oxidized to ferric iron and ejected to hydrolyze and
form an Fe(III) oxyhydroxide precipitate. This, in turn, allows some structural
OH groups in the octahedral sheet to rotate toward the now-vacant former
Fe(II) sites, the OH protons thereby being rendered less effective at repelling
the surviving K + between the biotite layers (Fig. 2.5). Under moderate leach-
ing conditions, muscovite transforms to dioctahedral smectite (see Problem
13 in Chapter 1), whereas biotite transforms to trioctahedral vermiculite and
goethite (or ferrihydrite). A possible reaction for this latter transformation is

K 2 [Si 6 Al 2 ]Mg 3 Fe(ID 3 2 o(OH)4(s) + 2.7Mg 2+ + 3.9 H 2 0(£)
(biotite)

+ 0.75 2 (g) = K L7 [Si 6 Al 2 ] Mg 57 Fe(III) .3 O 20 (OH) 4 (s)

(vermiculite)

+ 2.7 FeOOH(s) + 0.3 K+ + 5.1 H+
(goethite)

(2.5)

Note that the layer charge (see Section 1.3), as evidenced by the stoi-
chiometric coefficient of K + , decreases from 2.0 in biotite to 1.7 in vermiculite
because of the oxidation of ferrous iron. Although this layer charge is balanced
by K + in Eq. 2.5, Mg 2+ is also a common interlayer cation in trioctahedral
vermiculite. Under intensive leaching conditions, biotite will transform to
kaolinite and goethite, as illustrated in Eq. 1.3. In this case, silica and Mg + are
lost to the soil solution along with K + . A comparison of Eqs. 1.3 and 2.5 shows
that kaolinite formation is favored by acidity (H + is a reactant) and inhibited
by soluble Mg + (a product), whereas vermiculite formation is inhibited by
acidity (H + is a product) and favored by soluble Mg + (a reactant).

The atomic structure of the feldspars is a continuous, three-dimensional
framework of tetrahedra sharing corners, as in quartz, except that some of the

40 The Chemistry of Soils

tetrahedra contain Al instead of Si, with electroneutrality thus requiring either
monovalent or bivalent metal cations to occupy cavities in the framework.
These primary minerals, the most abundant in soils, have repeating units of
either AIS13 OJJ~, with Na + or K + used for charge balance, or AI2 S12 8 ~,
with Ca + used for charge balance (Table 2.3). Solid solution among the three
minerals thus formed is extensive, with that between albite and anorthite
being known as plagioclase, whereas that between albite and orthoclase termed
simply alkali feldspar. The weathering of these abundant minerals in soils
occurs on timescales of millennia.

Figure 2.6 illustrates this last point with measurements of the amounts
of hornblende, plagioclase, and K-feldspar remaining (relative to quartz) in
the surface (A in Fig. 2.6) and subsurface (B and C in Fig. 2.6) horizons of a
soil chronosequence comprising Entisols, Mollisols, Alfisols, and Ultisols, the
members of which ranged in age from two centuries to 3000 millennia, as
determined by radioactive isotope dating methods. The graph in Figure 2.6
indicates that all three primary silicates were depleted during the first few
hundred millennia of weathering and that the overall rate of depletion was in
the order of hornblende > plagioclase > K-feldspar, with the surface horizon

1.2

1.0 -

£ 0.8 -

0.6 -

0.4 -

0.2 -

0.0

■ □ Hornblende
O Plagioclase
▼ V K-Feldspar

1.0 2.0

Soil Age (Myr)

3.0

Figure 2.6. Depletion of amphiboles (hornblende) and feldspars (plagioclase and K-
feldspar) with time during soil weathering. The ordinate is the content of primary
silicate in the soil relative to that of quartz, which is assumed to be conserved. Data
from White, A. F., et al. (1995) Chemical weathering rates of a soil chronosequence on
granitic alluvium: I. Geochim. Cosmochim. Acta 60:2533-2550.

Soil Minerals 41

showing more depletion than subsurface horizons. These trends are in keeping
with the smaller Si-to-O ratio in amphiboles than in feldspars (see Section 1.3)
and with the more intense weathering expected near the top of a soil profile.
Feldspar dissolution provides metal cations to the soil solution that figure
importantly in the neutralization of acidic deposition on soils, the nutrition of
plants, and the regulation of CO2 concentrations. Bacteria and fungi enhance
this dissolution process through the production of organic ligands (Eq. 1.4)
and protons, particularly in the case of K-feldspar, which then serves as a
source of K. Feldspars weather eventually to kaolinite (Eq. 1.2) or gibbsite (see
Problem 12 in Chapter 1), but smectite also is a common secondary mineral
product (see Problem 13 in Chapter 1):

5 KAlSi 3 8 (s) +4 H+ + 16 H 2 0(£)
(orthoclase)

= K[Si 7 Al]Al 4 02o(OH)4(s) +8 Si(OH)° + 4 K+ (2.6)

(beidellite)

Note the consumption of protons and the production of silicic acid and soluble
cations, as also observed in Eq. 1.2.

The general characteristics of primary silicate weathering illustrated by
eqs. 1.2, 1.3, 1.4, 2.5, and 2.6 can be summarized as follows:

• Conversion of tetrahedrally coordinated Al to octahedrally
coordinated Al

• Oxidation of Fe(II) to Fe(III)

• Consumption of protons and water

• Release of silica and metal cations

In the case of the micas, there is also an important reduction of layer
charge accompanying the first two characteristics (Eq. 2.5 and Problem 13
in Chapter 1). From the weathering sequence in Table 1.7, one can conclude
that soil development renders tetrahedral Al and ferrous iron unstable in
response to continual throughputs of oxygenated fresh water (i.e., rainwater),
which provides protons and, in return, receives soluble species of major ele-
ments. If these latter elements are not leached, the secondary silicates that
characterize the intermediate stage of weathering will form, as in Eq. 2.6. If
leaching is extensive, desilicated minerals characteristic of the advanced stage
of weathering will begin to predominate in the clay fraction, as in eqs. 1.2
and 1.3.

2.3 Clay Minerals

Clay minerals are layer-type aluminosilicates that predominate in the clay
fractions of soils at the intermediate to advanced stages of weathering. These

42 The Chemistry of Soils

minerals, like the micas, are sandwiches of tetrahedral and octahedral sheet
structures like those in Figure 2.3. This bonding together of the tetrahedral
and octahedral sheets occurs through the apical oxygen ions in the tetrahedral
sheet and produces a distortion of the anion arrangement in the final layer
structure formed. The distortion occurs primarily because the apical oxygen
ions in the tetrahedral sheet cannot be fit to the corners of the octahedra
to form a layer while preserving the ideal hexagonal pattern of the tetra-
hedra. To fuse the two sheets, pairs of adjacent tetrahedra must rotate and
thereby perturb the symmetry of the cavities in the basal plane of the tetrahe-
dral sheet, altering them from hexagonal to ditrigonal (Fig. 2.3). Besides this
distortion, the sharing of edges in the octahedral sheet shortens them (Pauling
Rule 3, Fig. 2.3). These effects occur in the micas and in the clay minerals, both
of whose atomic structures were first worked out by Linus Pauling (see Special
Topic 2, at the end of this chapter). The clay minerals are classified into three
layer types, distinguished by the number of tetrahedral and octahedral sheets
combined to form a layer, and further into five groups, differentiated by the

1:1 Layer Type

2:1 Layer Type

Figure 2.7. "Ball-and-stick" drawings of the atomic structures of 1: 1 and 2: 1 layer- type
clay minerals.

Soil Minerals 43

Table 2.4

Clay minera

1 groups. 3

Layer

charge

Group

Layer type

(*)

Kaolinite

1:1

< 0.01

Illite

2:1

1.2-1.7

Vermiculite

2:1

1.2-1.8

Smectite c

2:1

0.4-1.2

Chlorite

2:1
with

hydroxide
interlayer

Variable

Typical chemical formula 6

[Si 4 ]Al 4 Oio(OH) 8 • nH 2 (n = or 4)
M x [Si 6 . 8 Al 1 . 2 ]Al 3 Feo.25Mgo.7502o(OH) 4
M x [Si 7 Al] Al 3 Feo.5Mg .5 O 20 (OH) 4
M x [Si 8 ]Al 3 .2Feo.2Mgo. 6 20 (OH) 4
(Al(OH) 2 .55) 4 [Si 6 . 8 Al 1 . 2 ]Al 3 . 4 Mgo.60 20 (OH) 4

"Guggenheim, S., et al. (2006) Summary of recommendations of nomenclature committees
relevant to clay mineralogy. Clays Clay Miner. 54:761-772.

[ ] indicates tetrahedral coordination; n = is kaolinite and n = 4 is halloysite; H2O = interlayer
water; M = monovalent interlayer cation.
'Principally montmorillonite and beidellite in soils.

extent and location of isomorphic cation substitutions in the layer. The layer
types are shown in Fig. 2.7, whereas the groups are described in Table 2.4.

The 1:1 layer type consists of one tetrahedral and one octahedral sheet.
In soil clays, it is represented by the kaolinite group, with the generic chemi-
cal formula [Si4]Ai40io(OH)8 • MH2O, where the element enclosed in square
brackets is in tetrahedral coordination and n is the number of moles of hydra-
tion water between layers. As is common for soil clay minerals, the octahedral
sheet has two thirds of its cation sites occupied (dioctahedral sheet). Normally
there is no isomorphic substitution for Si or Al in kaolinite group minerals,
although low substitution of Fe for Al is sometimes observed in Oxisols, and
poorly crystalline varieties of kaolinite are thought to have some substitution
of Al for Si. Kaolinite group minerals are the most abundant clay minerals in
soils worldwide, although, as implied in Table 1 .7, they are particularly charac-
teristic of highly weathered soils (Ultisols, Oxisols). Their typical particle size
is less than 10 |xm in diameter (fine silt and clay fractions), and their specific
surface area ranges from 0.5 to 4.0 x 10 m kg , with the larger values being
measured for poorly crystalline varieties. Aggregates of these clay minerals
are observed as stacks of hexagonal plates if the layers are well crystallized,
whereas elongated tubes with inside diameters on the order of 15 to 20 |xm
or more (or sometimes spheroidal particles) are found if the layers are poorly
crystallized. (If the repeating structure based on the chemical formula of a
solid phase persists throughout a molecular-scale region with a diameter that
is at least as large as 3 nm, the solid phase is said to be crystalline. If struc-
tural regularity does not exist over molecular-scale distances this large, the
solid phase is termed poorly crystalline.) The subgroup associated with the

44 The Chemistry of Soils

tubular morphology contains interlayer water (n = 4 in the chemical for-
mula) and is named halloysite (Table 2.4). Halloysite tends to be found under
conditions of active weathering abetted by ample water, but it can dehydrate
eventually to form more well- crystallized kaolinite (n = in the chemical
formula). The tubular morphology is thought to be an alternative structural
response to tetrahedral-octahedral sheet misfit, wherein the tetrahedral sheet
rolls around the octahedral sheet because interlayer water has prevented the
tetrahedra from rotating as they do in kaolinite.

The oxygen ions in the basal plane of the tetrahedral sheet in kaolinite are
bonded to a pair of Si 4+ , whereas the apical oxygen ions are bonded to one Si 4+
and two Al 3+ in consonance with Pauling Rule 2 (Fig. 2.7). Similarly, the OH
ions in the basal plane of the octahedral sheet are bonded to two Al 3+ , as are
the OH in the interior of the layer. Therefore, if the layer were infinite in lateral
extent, it would be completely stable according to the Pauling rules. However,
the oxygen and OH ions at the edge surfaces of a finite layer structure will
always be missing some of their cation bonding partners, leading to the ability
to bind additional cationic charge, as discussed for free oxyanions in Section
2.1. An exposed oxygen ion bound to a single Si 4+ at an edge, for example,
bears an excess charge of —1.0 vu and, therefore, requires a cation partner with
a bond valence of 1.0 vu to be stable. This requirement can be met easily if a
proton from aqueous solution becomes bound to the oxygen ion (Fig. 2.8). The
situation is not as simple for an exposed OH ion, which bears an excess charge
of -0.5 vu and thus requires a cation partner with a bond valence of 0.5 vu to
be stable. Attraction of a proton from aqueous solution leads to the formation

of OH 2 at the edge surface, which is still not stable. The excess positive

1/2—

charge created can be neutralized in principle by a neighboring OH 2 , but
this possibility clearly will be affected by soil solution pH. It turns out that the

< 5.2 > 5.2

Figure 2.8. Atomic structure at the edge of a kaolinite layer exposed to water. As pH
drops below 5.2, exposed Si— 0~ and Al-OH ' each protonate to form Si— OH and

+ 1/2

Al— OH 2 respectively.

Soil Minerals 45

affinity of the kaolinite edge surface for protons leads to an electrically neutral
condition at pH 5.2, with the surface being increasingly positively charged
below this pH value and increasingly negatively charged above it. As was the
case for the oxyanions considered in Section 2.1, failure to satisfy the Pauling
Rules leads to reactivity with protons — in the present case, those in the soil
solution contacting the edge surface of kaolinite.

The 2:1 layer type has two tetrahedral sheets that sandwich an octahedral
sheet (Fig. 2.7). The three soil clay mineral groups with this structure are Mite,
vermiculite, and smectite. If a, b, and c are the stoichiometric coefficients of
Si, octahedral Al, and Fe(III) respectively, in the chemical formulas of these
groups, then

x = moles Al substituting for Si + moles Mg and Fe(II)

substituting for Al (2.7)

= (8 - a) + (4 - b - c) = 12 - a - b - c (2.8)

is the layer charge, the number of moles of excess electron charge per chem-
ical formula that is produced by isomorphic substitutions. As indicated in
Table 2.4, the layer charge decreases in the order illite > vermiculite > smectite.
The vermiculite group is further distinguished from the smectite group by a
greater extent of isomorphic substitution in the tetrahedral sheet. Among the
smectites, two subgroups also are distinguished in this way, those for which the
substitution of Al for Si exceeds that of Fe(II) or Mg for Al (called beidellite;
Eq. 2.6), and those for which the reverse is true (called montmorillonite) . The
smectite chemical formula in Table 2.4 represents montmorillonite. In any of
these 2:1 minerals, the layer charge is balanced by cations that reside near or in
the ditrigonal cavities of the basal plane of the oxygen ions in the tetrahedral
sheet (Figs. 2.3 and 2.9). These interlayer cations are represented by M in the
chemical formula of smectite (Table 2.4).

The layer charge in Eq. 2.7 is closely related to the structural charge, cjq,
defined by the equation

cr = -(x/M r ) x 10 3 (2.9)

where x is the layer charge and M r is the relative molecular mass (see the
Appendix). The units of oq are moles of charge per kilogram (mol c kg -1 , see
the Appendix). The value of M r is computed with the chemical formula and
known relative molecular masses of each element that appears in the formula.
For example, in the case of the smectite with a chemical formula that is given
in Table 2.4,

M r = 8 (28.09) +3.2 (27) +0.2 (55.85) +0.6 (24.3)
Si Al Fe Mg

+ 24 (16) +4(1) = 725 Da
O H

46 The Chemistry of Soils

Therefore, according to Eq. 2.7 and the range of x in Table 2.4, oq varies
between -0.7 and —1.7 mol c kg for smectites. In a similar way, o$ is found to
vary from -1.9 to -2.8 mol c kg -1 for illites, and from —1.6 to -2.5 mol c kg -1
for vermiculites. These minerals are significant sources of negative structural
charge in soils.

Particle sizes of the 2:1 clay minerals place them in the clay fraction, with
illite and vermiculite typically occurring in larger aggregates of stacked layers
than smectite, for which lateral particle dimensions around 100 to 200 nm
are characteristic. Specific surface areas of illite average about 10 m kg ,
whereas those of vermiculite and smectite can approach 8 x 10 m kg ,
depending on the number of stacked layers in an aggregate. The origin of
this latter value, which is very large (equivalent to 80 ha kg -1 clay mineral),
can be seen by calculating the specific surface area (a s ) of an Avogadro number
of unit cells (unit cells are the basic repeating entities in a crystalline solid)
forming a layer of the smectite featured in Table 2.4:

a s = surface area per unit cell x (Na/M,-) x 10
= 0.925 nm 2 per cell x 10~ 18 m 2 nm" 2
6.022 x 10 23 .. 3

cells x 10 3 gkg l

725 g
= 7.6 x 10 5 m 2 kg -1

where Na = 6.022 x 10 23 is the Avogadro constant (also denoted L; see the
Appendix) and the surface area of the smectite unit cell is calculated as twice
the nominal surface area of one face in the crystallographic ab plane (i.e., twice
0.4627 nm), which is valid for a crystal layer with lateral dimensions (100-
200 nm) that greatly exceed its thickness (only 1 nm for 2:1 clay minerals).
This very large specific surface area pertains to particles that comprise a single
crystal layer 100 to 200 nm in diameter. If, instead, n such layers are stacked
to build an aggregate, the specific surface area is equal to the value found
previously divided by n, because stacking a pair of layers together necessarily
consumes the area of one basal surface of each. In aqueous suspensions, n = 1
to 3 for smectites with monovalent interlayer cations (e.g., Li + , Na + , K + ),
whereas dehydrated smectites are found in aggregates with about 10 times
as many stacked layers. Thus a s for smectite aggregates can vary from nearly
80 ha kg -1 to around 4 ha kg -1 .

The 2:1 layer type with a hydroxide interlayer is represented in soils
by vermiculite or smectite with an Al-hydroxy polymer cation in the inter-
layer regions (Table 2.4), with the collective name for these subgroups being
pedogenic chlorite. Formation of these clay minerals is mediated by acidic
conditions, under which Al + is released by mineral dissolution, hydrolyzes,
and replaces the interlayer cations in vermiculite or smectite, with incom-
plete hydrolysis resulting in a cationic Al— hydroxy polymer with a fractional

Soil Minerals 47

stoichiometric coefficient for OH < 3 instead of Al(OH)3. Pedogenic chlorite
is characteristic of highly weathered soils, such as Ultisols and Oxisols, but
also is found in Alfisols and Spodosols. Whenever a complete, isolated gibbsite
sheet [Al(OH)3] forms in the interlayer region, the resulting mineral is termed
simply chlorite.

Structural disorder in the 2:1 clay minerals listed in Table 2.4 is induced
through isomorphic substitutions in their octahedral sheets (tables 1.5 and
2.4). More pronounced structural disorder exists in silica and in alumi-
nosilicates that are freshly precipitated in soils undergoing active weathering,
because these solid phases typically are excessively hydrated and poorly crys-
talline. Even among the more crystalline soil clay minerals, there is also wide
variability in nanoscale order, with disorder created by dislocations (micro-
crevices between offset rows of atoms) and irregular stacking of crystalline
unit layers. This kind of disorder exists, for example, in kaolinite and illite
group minerals.

Poorly crystalline hydrated aluminosilicates, known collectively as imogo-
lite and allophane (Table 1.3), are common in the clay fractions of soils formed
on volcanic ash deposits (Andisols), but they can also be derived from many
other kinds of parent material (e.g., granite or sandstone) under acidic con-
ditions, regardless of temperature regime, if soluble Al and Si concentrations
are sufficiently high and Al is not complexed with organic ligands, which
interferes with precipitation (Eq. 1.4). Imogolite, having the chemical formula
S12AI4O10 -5H20, contains only octahedrally coordinated Al and exhibits a
slender tubular particle morphology. The tubes are several micrometers long,
with a diameter of about 2 nm, exposing a defective, gibbsitelike outer surface.
The specific surface area of imogolite is comparable with — or even greater
than — that of smectite. A surface charge develops from unsatisfied oxygen ion
bond valences, similar to what occurs in kaolinite group minerals, but the pH
value at which imogolite is electrically neutral is much higher (pH ~ 8.4).

Allophane has the general chemical formula SiyA^Og-i^}' ■ « H2O, where
1-6 < y < 4, n >5 (Table 1.3). Thus it exhibits Al-to-Si molar ratios both
larger and smaller than imogolite (y = 2) and it contains more bound water. Its
specific surface area is also comparable with that of smectite and, like this latter
clay mineral, a structural charge in allophane is possible because of isomorphic
substitution of Al for Si in tetrahedral coordination, and charge development
from unsatisfied oxygen ion bond valences occurs just as it does in kaolinite
and imogolite. The pH value at which the protonation mechanism results in an
electrically neutral surface varies inversely with the value of y in the chemical
formula, decreasing from about pH 8.0 for y = 2 (termed the proto-imogolite
allophane species) to about pH 5.4 for y = 4 (termed the defect kaolinite
allophane species). Evidently, the increasing presence of Al results in stronger
protonation, thus requiring higher pH for electrical neutrality, whereas that
of Si has the opposite effect. The atomic structure of allophane is not well
understood, but is thought in most cases to consist of fragments of imogolite
combined with a 1:1 layer- type aluminosilicate that is riddled with vacant ion

48 The Chemistry of Soils

sites and doped with Al in tetrahedral coordination. This defective structure
promotes a curling of the layer into the form of hollow spheroids 3 to 5 nm in
diameter with an outer surface that can contain many microapertures through
which molecules or ions in the soil solution might invade. As this structural
concept suggests, allophane often is found in association with kaolinite group
minerals, especially halloysite.

Poorly crystalline kaolinite group minerals have been observed to pre-
cipitate in bacterial biofilms, which are layered organic matrices comprising
extracellular polymers that enmesh bacterial cells along with nutrients and
other chemical compounds. When minerals form in biofilms, the biofilms
are termed geosymbiotic microbial ecosystems to emphasize the close spatial
relationship that exists between the minerals and the microbes. Under highly
anaerobic conditions at circumneutral pH in freshwater biofilms that contain a
variety of different bacteria and filamentous algae, clay-size, hollow, spheroidal
particles identified as poorly crystalline kaolinite group minerals appear to
nucleate and grow on bacterial surfaces as a product of feldspar weathering
(see Eq. 1.2). Similar observations have been reported for 2:1 layer-type clay
minerals under active weathering conditions.

The 2:1 clay minerals, as well as pedogenic chlorite, imogolite, and
allophone, all are expected to weather by hydrolysis and protonation to
form kaolinite group minerals according to the Jackson-Sherman weathering
sequence (Table 1.7):

K[Si 7 Al]Al 4 2 o(OH)4(s) +H+ + — H 2 0(£)

(beidellite) 2

= -[Si 4 ]Al 4 Oio(OH) 8 +2 Si(OH)2 + K+ (2.10a)

(kaolinite)

(Al(OH) 2 . 5 )2[Si7Al]Al 4 2 o(OH)4(s) +10 H 2 0(£) (2.10b)

(pedogenic chlorite)

= [Si 4 ]Al 4 Oio(OH) 8 (s) + 3 Al(OH) 3 (s) + 3 Si(OH)°

(kaolinite) (gibbsite)

Si 3 Al 4 Oi 2 • nH 2 0(s)+-H 2 0(£)

(allophane) ^

3
= - [Si 4 ]Al 4 O 10 (OH) 8 (s)+Al(OH) 3 (s)+nH 2 O(£) (2.10c)

4 (kaolinite) (gibbsite)

Each of these reactions requires acidic conditions that are favored by fresh-
water and good drainage. The pedogenic chlorite reacting in Eq. 2.10b is an
example of hydroxy -interlay er beidellite (x = 1.0), whereas hydroxy -interlay er

Soil Minerals 49

vermkulite (x = 1.8) is shown in Table 2.4. The allophane reactant in Eq. 2.10c
is a defect kaolinite species.

2.4 Metal Oxides, Oxyhydroxides, and Hydroxides

Because of their great abundance in the lithosphere (Table 1.2), aluminum,
iron, manganese, and titanium form the important oxide, oxyhydroxide, and
hydroxide minerals in soils. They represent the climax mineralogy of soils, as
indicated in Table 1.7. The most significant of these minerals, all of which are
characterized by small particle size and low solubility in the normal range of
soil pH values, can be found in Table 2.5, with representative atomic structures
of some of them depicted in figures 2.9 and 2.10. For each type of metal
cation, the Pauling Rules would indicate primarily octahedral coordination
with oxygen or hydroxide anions.

Gibbsite [y-Al(OH)3], the only Al mineral listed in Table 2.5, is found
commonly in Oxisols, Ultisols, Inceptisols, and Andisols, forming paral-
lelepipeds 50 to 100 nm in length under conditions of warm climate and
intense leaching that lead to Si removal from clay minerals and primary sil-
icates, especially feldspars (see Table 1.7; Eqs. 2.10b, c; and Problem 12 in
Chapter 1). Isomorphic substitutions do not appear to occur in this mineral.
Inorganic anions, such as carbonate and silica, and organic ligands, includ-
ing humic substances, disrupt the formation of gibbsite by complexing Al 3+
(e.g., Eq. 1.7), and promote instead the precipitation of poorly crystalline Al
oxyhydroxides with large specific surface areas (10— 60 ha kg ). These highly
reactive, disordered polymeric materials contribute significantly to the forma-
tion of stable aggregates in soils, often coating particle surfaces or entering
between the layers of 2:1 layer-type clay minerals to form hydroxy- interlayer
species (Table 2.4 and Eq. 2.9b).

Table 2.5

Metal oxides, oxyhydroxides, and hydroxides found commonly in soils.

Chemical

Name

formula 3 Name

formula 3

Rutile

Ti02 Hematite

a-Fe203

Birnessite

M x Mn(lV) a Mn(III)i,A c o!j Lepidocrocite

y-FeOOH

Ferrihydrite

FeioOi5-9H20 Lithiophorite

LiAl 2 (OH) 6 Mn(iV) 2
Mn(III)0 6

Gibbsite

y-Al(OH) 3 Maghemite c

y-Fe 2 3

Goethite

a-FeOOH Magnetite

FeFe 2 O4

a y denotes cubic close- packing of anions, whereas a denotes hexagonal close-packing.

M = monovalent interlayer cation, x = b + 4c, a + b + c = 1, A =

= cation vacancy.

c Some of the Fe(III) is in tetrahedral coordination.

50 The Chemistry of Soils

OH"

Figure 2.9. "Ball-and-stick" drawing of the atomic structure of gibbsite [y-Al(OH)3]

Gibbsite is a dioctahedral mineral comprising edge-sharing Al(OH)6 in
stacked sheets that are held together as an aggregate by hydrogen bonds that
form between opposing OH groups oriented perpendicularly to the basal
planes of the sheets. Hydrogen bonds also link the OH groups along the edges
of the cavities lying within a single sheet (Fig. 2.9), adding to the distortion
of the octahedra that is produced by the sharing of edges (Pauling Rule 3 and
Fig. 2.3). According to Pauling Rule 2, the bond strength of Al 3+ octahedrally
coordinated to hydroxide ions is 0.5 and, therefore, each OH - in gibbsite
should be bonded to a pair of Al 3+ , as indicated in Fig. 2.9 for the bulk
structure. At the edges of a sheet, however, pairs of hydroxyls are exposed that

Figure 2.10. Polyhedral depiction of the atomic structure of goethite, with the double
chains of Fe(III) octahedra lying perpendicular to the plane of the figure.

Soil Minerals 51

have unsatisfied bond valences. These hydroxyls lie along unshared octahedral
edges and are located approximately 0.197 nm from the Al + to which they
are coordinated, yielding an associated bond valence of 0.422 vu according
to Eq. 2.4. This leaves an unsatisfied bond valence equal to — 0.578 vu on
each exposed hydroxyl. Adsorption of a proton by one OH, following the
paradigm outlined for kaolinite edge surfaces (Fig. 2.8), then yields a more
stable configuration of the hydroxyl pairs, which can be stabilized even further
by hydrogen bonds with nearby water molecules in the soil solution. The pH
value at which an electrically neutral gibbsite edge surface occurs turns out to
be about 9.0, implying that this mineral bears a net positive charge over the
entire normal range of soil pH values. By contrast, the edge surfaces of clay
minerals typically bear a net negative charge above pH 5 to 7, depending on
the type of clay mineral, again illustrating the stronger protonation of Al-OH
groups relative to Si-OH groups that are exposed on edge surfaces.

Among the iron minerals listed in Table 2.5, goethite (a-FeOOH, named in
honor of the German polymath, Johann Wolfgang von Goethe, who described
iron oxides in the red soils of Sicily during the late 18th century) is the most
abundant in soils worldwide, especially in those of temperate climatic zones. Its
atomic structure (Fig. 2.10) comprises double chains of edge-sharing, distorted
octahedra having equal numbers of O and OH - coordinated to Fe , with
each double chain then sharing octahedral corners with neighboring double
chains. As discussed in Section 2.1, the Pauling Rules, supplemented by the
more general concept of bond valence, are satisfied in this structure only
because of hydrogen bonding between OH and O (Fig. 2.2). In soils, goethite
crystallizes with relatively small particle size, exhibiting specific surface areas
that range from 2 to 20 ha kg -1 .

Soils in warm, dry climatic zones tend to contain hematite (a-Fe203,
named for its red-brown hue) in preference to goethite (which has a yellow-
brown hue). Hematite has the same atomic structure as the Al oxide mineral
corundum, mentioned in Section 2.1, with both having hexagonal rings of
edge-sharing octahedra arranged in stacked sheets that are themselves linked
through face-sharing octahedra. All this polyhedral sharing pushes the Fe +
cations closer together and produces considerable structural distortion, as
would be predicted from Pauling Rule 3 . Hematite particles tend to have rather
low specific surface areas (<10hakg ). Substantial isomorphic substitution
of Al for Fe can occur in both goethite and hematite, the upper limit for the
Al-to-(Al + Fe) molar ratio being 0.33 in goethite and half of this value in
hematite. Aluminum substitution in these minerals is favored in soils under
acidic conditions that produce abundant soluble Al without the interference
of complexation by organic ligands or silica.

If organic ligands — especially humic substances — or soluble silica are at
significant concentrations, then the crystallization of goethite or hematite is
inhibited and poorly crystalline Fe(III) oxyhydroxides precipitate instead. This
situation is especially characteristic of the rhizosphere, resulting in the for-
mation of root-associated Fe(III) mineral mixtures known as iron plaque.

52 The Chemistry of Soils

Ferrihydrite (FeioOis • 9H20, an approximate chemical formula, because up
to half of the H may be in hydroxide ions, not water) is the most common of
these materials, found typically in soils where biogeochemical weathering is
intense, soluble Fe(II) oxidation is rapid, and water content is seasonally high
(e.g., Andisols, Inceptisols, and Spodosols). This mineral, often detected along
with goethite in soils, exhibits varying degrees of ordering of its Fe(III) octa-
hedra, with many structural defects, and spheroidal particle diameters of a few
nanometers, leading to specific surface areas of 20 to 40 ha kg - ' . Ferrihydrite
can precipitate abiotically from oxic soil solutions at circumneutral pH, but
its formation tends to be mediated by bacteria at acidic pH or under anaero-
bic conditions that slow Fe(II) oxidation significantly. Even at circumneutral
pH under oxic conditions, bacterial cell walls can nucleate ferrihydrite (and
goethite) precipitation after complexing dissolved Fe + cations and, in some
cases, producing organic polymers that constrain precipitation to occur near
the cell surface. Bacteria that thrive within biofilms either in highly acidic oxic
environments, or in anaerobic environments at circumneutral pH, can oxidize
Fe(II) enzymatically and rapidly enough to produce ferrihydrite at rates well
above those for abiotic pathways. The resulting poorly crystalline mineral is
encapsulated within extracellular organic polymers that keep it from fouling
the bacterial surface while it also serves as fortification against predation of the
organism. When polymeric matrices become fully encrusted with ferrihydrite
within this geosymbiotic microbial ecosystem, they are eventually abandoned
by the bacteria, which then begin to manufacture a new biofilm.

Magnetite [Fe(II)Fe(III)204], a mixed-valence iron oxide, contains Fe +
and half of its Fe 3+ in octahedral coordination with O 2- , with the remaining
Fe 3+ being in tetrahedral coordination. This mineral, named for its magnetic
properties, is widespread in soils and can form both abiotically (e.g., inherited
from soil parent material, or precipitated during the incongruent dissolu-
tion of ferrihydrite promoted by a reaction with dissolved Fe 2+ cations) and
biogenically (e.g., within magnetotactic bacteria that utilize this mineral for
orientation and migration in the earth's magnetic field, or as a secondary
precipitate under anaerobic conditions following the weathering of ferrihy-
drite by bacteria that oxidize organic matter). Maghemite (y-Fe203), another
magnetic mineral, is also widespread in soils of warm climatic zones, forming
through the oxidation of magnetite or from the intense heating of goethite and
ferrihydrite, as produced by fire. Like goethite, hematite, and ferrihydrite, Al
substitution, with an upper limit as high as found for goethite, occurs in both
magnetite and maghemite, the latter commonly arising from a heat-promoted
transformation of Al-substituted goethite.

Another mixed-valence mineral that can be formed by either abiotic or
bacterially mediated incongruent dissolution of ferrihydrite under anaerobic
conditions is green rust [(A • nH^O) Fe(III) x Fe(II)y(OH)3 X +27-£]> which
comprises a ferric-ferrous hydroxide sheet bearing a positive structural charge
(because of ferric iron) that is balanced by hydrated anions (A -nri^OXsuch
as chloride (x = 1, y = 3, £ = 1), sulfate, or carbonate (x = 2, y = 4, £ = 2),

Soil Minerals 53

which reside in the interlayer region, analogous to the interlayer cations that
balance the negative structural charge in 2:1 layer-type clay minerals (see
Section 2.3 and Table 2.4). Also in parallel to the 2:1 clay minerals, individual
sheets stack to form aggregates, with the stacking arrangement of the sheets
being determined by the nature of the interlayer anion. Green rust occurs
under alkaline conditions in poorly drained, biologically active soils that are
subject to anaerobic conditions because of high water content (hydromorphic
soils).

Birnessite [M x Mn(YV) a Mn(lll)yA c 02, where M is a monovalent inter-
layer cation, a + b + c = 1, and ▲ is an empty cation site in the octahedral
sheet] is the most common manganese oxide mineral in soils, where it is
often observed in fine-grained coatings on particle surfaces. Like gibbsite, it
is a layer-type mineral with sheets that comprise mainly Mn O^ octahedra,
but with significant isomorphic substitution by Mn 3+ (0 < b < 0.3 ) and a gen-
erous population of cation vacancies (0 < ▲ < 0.2), both of which induce a
negative structural charge. In practice, isomorphic substitutions tend to offset
cation vacancies, such that a range of birnessites exists, varying from those
with only Mn 3+ substitution (triclinic birnessite) to those with only cation
vacancies (8-MnC>2 or vernadite) . The resulting layer charge, x = b + 4c, is
compensated by protons and hydrated metal cations, including both Mn +
and Mn , that reside in the interlayer region, particularly near cation vacan-
cies, each of which bears four electronic charges in the absence of protonation

Figure 2.11. Polyhedral depiction of the local atomic structure in birnessite, showing
a cation vacancy with charge-balancing, solvated interlayer cations (Mn + on top and
K + on the bottom). Visualization courtesy of Dr. Kideok Kwon.

54 The Chemistry of Soils

(Fig. 2.11). The layer charge is quite variable, but values near 0.25 are com-
monly observed, implying er ~ —3 mol c kg (Eq. 2.8), which is comparable
with the negative structural charge observed for 2:1 clay minerals. Birnes-
site typically forms poorly crystalline particles comprising a small number of
stacked, defective sheets less than 10 nm in diameter. Specific surface areas
of these particles range from 3 to 25 ha kg , a range that is similar to soil
goethites.

Birnessites precipitate in soils as a result of the oxidation of dissolved
Mn , which, if it occurs abiotically, is orders of magnitude slower than that
of dissolved Fe 2+ at circumneutral pH in the presence of oxygen. Bacteria and
fungi that catalyze the oxidation of Mn(II) under these conditions enzymati-
cally and rapidly (timescales of hours for bacterial oxidation vs. hundreds of
days for abiotic oxidation) are widespread in nature, leading to the conclusion
that soil birnessites are primarily of biogenic origin. Similar to bacterio-
genic ferrihydrite, birnessites produced by bacteria often are found enmeshed
within biofilms, where these highly reactive, poorly crystalline nanoparti-
cles may serve to impede predation and sequester both toxic and nutrient
metal cations. Geosymbiotic microbial ecosystems thus play an important
role in the biogeochemical cycling of Al, Fe, and Mn in soils and natural
waters.

2.5 Carbonates and Sulfates

The important carbonate minerals in soils include calcite (CaC0 3 ), dolomite
[CaMg(C0 3 ) 2 ],nahcolite(NaHC0 3 ),trona [Na 3 H(C0 3 ) 2 • 2 H 2 0], and soda
(Na2C0 3 • 10 H2O). Calcite may be, and dolomite appears often to be, a pri-
mary mineral in soils. Secondary calcite that precipitates from soil solutions
enriched in soluble Mg coprecipitates with MgC0 3 to form magnesian calcite,
Cai-yMgyCC^, with the stoichiometric coefficient)' typically wellbelowO. 10.
This mode of formation accounts for much of the secondary Mg carbonate
found in arid-zone soils. Like secondary metal oxides and hydroxides, sec-
ondary Ca/Mg carbonates can occur as coatings on other minerals, in nodules
or hardened layers, and as clay or silt particles. They are important repositories
of inorganic C in Aridisols and Mollisols.

Pedogenic calcites are normal weathering products of Ca-bearing primary
silicates (pyroxenes, amphiboles, feldspars) as well as primary carbonates.
Their formation is favored in the rhizosphere, where bacteria and fungi medi-
ate calcite precipitation, both through nucleation around excreted Ca + that
has been complexed by cell walls and through increases in soil solution pH
(>7.2) induced by enzymatically catalyzed reduction of nitrate, Mn, Fe, and
sulfate or methane production, the last process being associated with pedo-
genic dolomite formation. As an example of primary mineral weathering to
produce secondary calcite, the feldspar anorthite (Table 2.3) maybe considered
as follows:

Soil Minerals 55

CaAl 2 Si 2 8 (s) + 0.5 Mg 2+ + 3.5 Si(OH)^ + C0 2 (g)
(anorthite)

= Cao.5tSi7.5Alo.5JAl3.5Mg,, 5 O 20 (OH) 4 (s) + CaC0 3 (s)
(smectite) (calcite)

+ 0.5 Ca 2+ + 5 H 2 0(£) (2.11)

This incongruent dissolution reaction takes advantage of soluble Mg and silica
available from weathering and of ubiquitous biogenic C0 2 in soils. Note that
the reaction products are favored by abundant C0 2 , because it is a reactant,
and are inhibited by abundant H 2 0, because it is one of the products. Thus,
calcite formation can be prompted by elevated C0 2 concentration.

The formation of calcite from the dissolution of primary carbonates also
is favored by abundant C0 2 , but not as a source of dissolved carbonate ions.
Instead, carbonic acid that is formed when C0 2 dissolves in the soil solution
serves as a source of protons to aid in the dissolution of primary calcite or
dolomite:

C0 2 (g) + H 2 0(£) = H 2 CO* = H+ + HC07 (2.12a)

CaC0 3 (s) + H+ = Ca 2+ + HCO~ (2.12b)

where H 2 CO| conventionally designates the sum of undissociated carbonic

acid (H 2 COS) and solvated C0 2 (C0 2 • H 2 0), because these two dissolved

'§)

species are very difficult to distinguish by chemical analysis (see Problem 15 in

Chapter 1). If soil leaching is moderate and followed by drying, the reaction
in Eq. 2.11b is reversed and secondary calcite forms. Note that this reversal is
favored by high pH (i.e., low proton concentration).

Calcium coprecipitation bivalent with Mn, Fe, Co, Cd, or Pb by sorption
onto calcite is not uncommon (see Table 1.5). The trace metals Zn, Cu, and
Pb also may coprecipitate with calcite by inclusion as the hydroxycarbon-
ate minerals hydrozincite [Zn3(OH)g(C03) 2 ], malachite [Cu 2 (OH) 2 C03],
azurite [Cu3(OH) 2 (C0 3 ) 2 ], or hydrocerrusite [Pb 3 (OH) 2 (C0 3 ) 2 ]. Under
anoxic conditions that favor Mn(II), Fe(II), and abundant C0 2 , rhodocrosite
(MnCOs) and siderite (FeCC>3) solid-solution formation is possible — in the
absence of inhibiting sorption of humus by the nucleating solid phase, which
also retards calcite precipitation. Green rust, the Fe(II)-Fe(III) hydroxy car-
bonate discussed in Section 2.4, can precipitate under these conditions as well,
with C0 3 - then being the interlayer anion.

Like secondary carbonates, Ca, Mg, and Na sulfates tend to accumu-
late as weathering products in soils that develop under arid to subhumid
conditions, where evaporation exceeds rainfall (Table 1.7). The principal min-
erals in this group are gypsum (CaSC>4 • 2 H 2 0), anhydrite (CaS04), epsomite
(MgS0 4 ■ 7 H 2 0), mirabilite (Na 2 S0 4 • 10H 2 O), and thenardite (Na 2 S0 4 ).
Gypsum, similar to calcite, can dissolve and reprecipitate in a soil profile that

56 The Chemistry of Soils

is leached by rainwater or irrigation water and can occur as a coating on soil
minerals, including calcite. The Na sulfates, like the Na carbonates, form at the
top of the soil profile as it dries through evaporation.

In highly acidic soils, sulfate, either produced through sulfide oxidation
or introduced by amendments (e.g., gypsum), can react with the abundant
Fe and Al in the soil solution to precipitate the minerals schwertman-
nite [Fe 8 8 (OH) 6 S0 4 ], jarosite [KFe3(OH) 6 (S0 4 )2], alunite [KAl 3 (OH) 6
(S0 4 ) 2 ], basaluminite [Al 4 (OH)i SO 4 • 5 H 2 0], or jurbanite (AlOHS0 4 • 5
H2O). These minerals, in turn, may dissolve incongruently to form ferrihy-
drite and goethite or gibbsite upon further contact with a percolating, less
acidic soil solution. Under similar acidic conditions, phosphate minerals such
as wavellite [Al 3 (OH) 3 (P0 4 ) 2 • 5 H 2 0], angellite [Al 2 (OH) 3 P0 4 ], barandite
[(Al,Fe)P0 4 • 2 H 2 0], and vivianite [Fe 3 (P0 4 ) 2 • 8 H 2 0] have been observed
in soils, with the latter requiring anoxic conditions to precipitate, whereas
the others require phosphoritic parent materials. As soil pH increases, Ca
phosphates such as apatite [Ca 3 (OH,F)(P0 4 ) 3 ] and octacalcium phosphate
[CasH 2 (P0 4 )6 -5 H 2 0] tend to form, particularly if soluble phosphate has
been introduced in abundance by soil amendments or wastewater percolation.

For Further Reading

Banfield, J. F., and K. H. Nealson (eds.). (1997) Geomicrobiology: Interactions
between microbes and minerals. The Mineralogical Society of America,
Washington, DC. The 13 chapters of this edited workshop volume
provide a fine introduction to the important roles played by microor-
ganisms in the formation and weathering of minerals in soils and aquatic
environments.

Dixon, J. B., and D. G. Schulze (eds.). (2002) Soil mineralogy with environmen-
tal applications. Soil Science Society of America, Madison, WI. Chapters
6 through 22 of this standard reference work on soil minerals may be
read to gain in-depth information about their structures, occurrence,
and weathering reactions.

Essington, M. E. (2004) Soil and water chemistry. CRC Press, Boca Raton,
FL. Chapter 2 of this comprehensive textbook may be consulted to learn
more about the atomistic details of soil mineral structures through its
many visualizations.

The following three specialized books offer a deeper understanding of the structure
and reactivity of minerals in natural soils and aquatic systems, including those
affected by pollution:

Cornell, R. M., and U. Schwertmann. (2003) The iron oxides. Wiley-VCH
Verlag, Weinheim, Germany. This beautifully produced, exhaustive trea-
tise on the iron oxides is an indispensable reference for anyone who wants
to know specialized information.

Soil Minerals 57

Cotter— Howells, J. D., L. S. Campbell, E. Valsami-Jones, and M. Batchelder.
(2000) Environmental mineralogy. The Mineralogical Society of Great
Britain & Ireland, London. This edited volume provides useful overviews
of the microbial mediation of mineral weathering, as well as of mineral
structure and reactivity in contaminated soil environments.

Giese, R. R, and C. J. van Oss. (2002) Colloid and surface properties of clays and
related minerals. Marcel Dekker, New York. A detailed, comprehensive
reference on the structure and colloidal properties of the clay minerals.

Problems

The more difficult problems are indicated by an asterisk.

1. Use Pauling Rule 2 to show that, in a stable mineral structure, a corner of
an Si— O tetrahedron can be bonded solely to one other Si-O tetrahedron,
but not solely to one other Al-O tetrahedron. For the latter case, show that
bonding the Si-O tetrahedron to an Al-O tetrahedron and one bivalent
cation having CN = 8 will satisfy Pauling Rule 2. [The feldspar mineral
anorthite (Table 2.3) is an example.]

*2. Oxygen ions exposed on the edge surfaces of a goethite crystallite can be
bonded to one, two, or three Fe 3+ ions in the bulk structure, depending
on how the particle surface has formed. Apply Pauling Rule 2 to estimate
the unsatisfied bond valence on each type of exposed O , taking the
average Fe-O bond length to be 0.204 nm. Then consider whether the
formation of singly or doubly protonated species of the three types of
surface oxygen ion would stabilize them in the sense of Pauling Rule 2.
Which of the protonated species is likely to be a very weak acid (poor
proton donor)? Which among them should be the strongest acid? {Hint:
Review the examples discussed for oxyanions and for the edge surfaces of
kaolinite and gibbsite in Sections 2.1, 2.3, and 2.4.)

*3. Oxygen ions on the basal planes of birnessite (Fig. 2.11) are bonded to
three Mn 4+ ions, whereas those exposed on the edge surfaces are bonded
either to one or two Mn . Use Pauling Rule 2 to examine the stability of
these three types of surface oxygen ion, taking the average Mn-O bond
length to be 0.192 nm. Consider whether protonation of any of the three
will improve its stability.

4. The octahedral cation vacancies in a sheet of birnessite bear two elec-
tronic charges on each of two equilateral triangles of oxygen ions, one
exposed at the top of the sheet and one at the bottom (see Fig. 2.11). This
distribution of negative structural charge suggests that bivalent cations
could adsorb on the triangular sites, with one such cation bound to each
side of a vacancy to satisfy charge balance. A birnessite produced by a
Pseudomonas species (soil and freshwater bacterium), with the chemical

58 The Chemistry of Soils

formula Nao.i5Mn(III)o.i7[Mn(IV)o.83Ao.i70 2 ], was observed to adsorb
Zn + to achieve a maximum Zn-to-Mn molar ratio equal to 0.43 ± 0.04.
Show that this molar ratio is consistent with Zn 2+ replacing all interlayer
Na + and Mn 3+ in binding to the triangular vacancy sites in the Mn oxide
sheets.

5. Calculate the structural charge (o"o, in moles of charge per kilogram) on
the following layer-type minerals, given their chemical formulas. Identify
each of the minerals in light of your results.

(a)Ki.5[Si 7 Al]Al3.ioFe(III)o.4oM go . 50 2 o(OH)4

(b) Nao.78[Si 8 ]Al2.92Fe(III)o.3oMg 78 O 20 (OH) 4
(c)Nao.i 7 Mn(IV)o.83Mn(III) . 17 2

6. Alumino-goethite [Fei_j,AL,,0(C)H)], ferri-kaolinite [Si4(Ali_. ) ,Fe. K )40io
(OH)s], magnesian calcite [Cai-yMgyCC^], mangano-siderite [Fei-y
Mn^Co3 ] , and barrandite [Ali-^FeyPC^ • 2 H 2 0] are examples of copre-
cipitated soil minerals, with the metal having the stoichiometric coeffi-
cient ;' being in the minor component. For each of these solids, rewrite the
chemical formula to indicate 1 — y moles of the major component mineral
combined with y moles of the minor component mineral. [The minor
component AlO(OH) in alumino-goethite is known as diaspore when it
occurs as a pure solid phase, and the two components of barrandite are
known as variscite (Al) and strengite (Fe).]

7. The table presented here lists mass-normalized steady-state congruent
dissolution rates at pH 5 and 25 °C for three silicate minerals of impor-
tance in soils. These data can be used to calculate an intrinsic dissolution
timescale,

r dis = (M r x dissolution rate) -1

where M r is the relative molecular mass of the dissolving mineral and the
dissolution rate is in units of moles per gram per second. The value of
tdis characterizes the timescale on which 1 mole of a mineral will dissolve
in water. Calculate t^is m years for the three minerals, then compare your
results with the trends expressed in Table 1.7.

Mineral Dissolution rate (mol g 1 s 1 )

Forsterite 5.7 x 10 -11

Hornblende 4.3 x 10" 14

Quartz 2.1 x 10" 16

8. Using the notation in Problem 6, write a balanced chemical reaction
for the incongruent dissolution of ferri-kaolinite having 2 mol% Fe(III)

Soil Minerals 59

substituted for Al. The principal products are goethite, gibbsite, and silicic
acid.

9. Orthoclase can weather to form kaolinite and gibbsite under humid trop-
ical conditions. Select a weathering mechanism, then write a balanced
chemical reaction for this transformation.

10. The weathering of biotite as shown in Eq. 2.5 is typical of temperate
humid regions. In tropical humid regions, the clay mineral product is
typically kaolinite, not vermiculite. Develop a balanced chemical reaction
for the weathering of biotite to form kaolinite and goethite by hydrolysis
and protonation.

* 1 1 . Develop a single chemical equation that describes a reaction among trona,

nahcolite, and CC>2(g). Which of the two Na carbonates would be favored
by increasing the CO2 partial pressure in soil?

12. Gypsum is added to an acidic soil containing the Al-saturated beidellite
featured in Eq. 2.10b. Develop a chemical equation that describes the
formation of Ca-saturated beidellite and jurbanite from the incongruent
dissolution of gypsum in the presence of Al-beidellite. This reaction could
improve soil fertility by providing exchangeable and soluble Ca as well as
by reducing the bioavailability of Al through precipitation.

13. Develop a balanced chemical reaction for the transformation of schwert-
mannite to goethite.

* 14. Generalize Eq. 2.10c to be a weathering reaction for allophane having the

general chemical formula given in Section 2.3. Determine the threshold
value of the stoichiometric coefficient y above which more kaolinite than
gibbsite will be produced by the weathering of allophane.

*15. Combine Eqs. 2.10b and 2.10c to derive a chemical reaction for the
weathering of allophane, ( S\yk\$Of 1 +iy -nE^O, to form pedogenic chlo-
rite. What conditions favor this reaction? (Hint: The value of y varies
from 1.6 to 4.0.)

Special Topic 2: The Discovery of the Structures of Clay Minerals

Near the end of his long life, Linus Pauling published an informal account of his
research — which took place more than 75 years ago — on the atomic structures of
clay minerals and oxides [reprinted with permission from the newsletter of The
Clay Minerals Society (pp. 25-27, CMS News, September 1990)]. Pauling, the
only person to receive two unshared Nobel Prizes, wasperhaps the greatest physical
chemist of the past century. His life achievements related to crystallography were
recorded by Pauling himself in the first and fifth chapters of a testimonial volume,
The Chemical Bond, edited by A. Zewail (Academic Press, New York, 1992), but

60 The Chemistry of Soils

the newsletter article provides a more focused tale of direct relevance to thepresent
chapter. Note that Pauling was only 28 when he formulated his rule for stable
crystal structures. Sterling B. Hendricks, mentioned in the article as Pauling's first
graduate student, went on to a distinguished career with the U.S. Department
of Agriculture in clay mineralogy and, later, plant physiology. His breakthrough
article in 1930 (with William H Fry) on the crystal structures of soil colloids has
been reprinted in a celebratory issue of the journal, Soil Science (Hendricks, S. B.,
and W. H. Fry (2006) The results of X-ray and microscopical examinations of
soil colloids. Soil Science, Supplement to Volume 171, June 2006, pp. S51-S73).

I have been interested in the clay minerals for nearly eighty years, and
I was pleased when Patricia Jo Eberl wrote to me, asking me to write
an account of the discovery of their structure.

My interest in minerals began in 1913, when I was 12 years old, a
year before it shifted to chemistry. At that time I collected a few min-
erals and read books on mineralogy. Then in the fall of 1922, a couple
of months after I had entered the Division of Chemistry and Chemi-
cal Engineering at the California Institute of Technology as a graduate
student and had been taught X-ray crystallography by Roscoe Gilkey
Dickinson, the first person to have obtained a Ph.D. degree from the
California Institute of Technology (1920). I determined with Dickin-
son the crystal structure of a mineral, molybdenite. This mineral was
interesting as the first one to be found in which a metal atom, with
ligancy 6, is surrounded by atoms at the corners of a trigonal prism,
rather than at the corners of an octahedron.

The X-ray-diffraction method of determining the structures of
crystals was a marvelous method. It was not then very powerful, how-
ever; nevertheless during the period around 1922, many crystal struc-
tures, the simpler ones, were discovered and thoroughly investigated.
For example, Sterling B. Hendricks and I made a careful redetermina-
tion of the structure of hematite and corundum that had been inves-
tigated earlier by W.L. Bragg (later Sir Lawrence Bragg), who when he
was a student had discovered the "Bragg equation." Sterling Hendricks
was my first graduate student. The X-ray laboratory of the California
Institute of Technology, which had been set up in 1917, was turned
over to me by Dickinson in 1924. By 19271 had become impatient, as a
result of having had to abandon the study of many minerals and other
inorganic crystals because of the limited power of X-ray crystallogra-
phy, at that time, to locate the atoms. Bragg had in 1926, in his effort
to determine the structures of some silicate minerals, formulated the
hypothesis that, in these crystals, the structure was often to some
extent determined by having the large anions of oxygen arranged in
cubic close packing or hexagonal close packing, with the metal ions
in the interstices. I had the idea that the use of auxiliary information
of this sort could make the X-ray technique more powerful. From

Soil Minerals 61

studying the known structures of two forms of titanium dioxide,
rutile and anatase, I recognized that they were similar in a remarkable
way. In each structure there are octahedra of six oxygen ions around
a titanium ion. (At that time I overemphasized the ionic character of
bonds in the oxide minerals.) In rutile each octahedron shares two
edges with adjacent octahedra, and in anatase each octahedron shares
four edges with adjacent octahedra. I surmised that in brookite, the
third form of titanium dioxide, there would also be octahedra, with
each octahedron sharing three edges with adjacent octahedra, and I
formulated two structures satisfying this hypothesis, and with all of
the octahedra in each structure crystallographically equivalent.

My second graduate student, James Holmes Sturdivant (Ph.D.
1928), made X-ray photographs of brookite and found that the
dimensions of the orthorhombic unit cell agreed reasonably well with
those that I had predicted from the interatomic distances in rutile and
anatase, in which the shared edges of the octahedral are shortened to
about 2.50 A from the average value about 2.8 A, and that the inten-
sities of the diffraction maxima were in reasonable agreement with
those predicted for one of the two structures, which is now accepted as
the structure of brookite. I also used the idea, based on the ionic radii
that I had published in the Journal of the American Chemical Society
in 1927, that in topaz, Al2SiC>4F2, there would be AIO4F2 octahedra
and SiC>4 tetrahedra, and in this way was able to locate atoms in this
orthorhombic crystal.

In 1929, after having studied some other minerals and applied this
method of predicting their structures and then checking by compar-
ison with the X-ray data, I published two papers on a set of principles
determining the structure of complex ionic crystals. One of these
rules is the Valence Rule. The valence of a cation is divided equally
among the bonds to the surrounding anions, and the sum of the bond
strengths of the bonds to each anion should be close to its negative
valence, usually within one quarter of a valence unit. In the papers
I started the argument by mentioning Bragg's use of the idea that
the oxygen (and fluorine) ions are often arranged in a close-packed
structure, but it turned out that for many silicates this arrangement
does not occur, whereas the principles of the coordination theory are
satisfied.

At that time, 1929, I became interested in the structure of mica,
and a few months later, of the chlorites and the clay minerals. I had
become interested in mica when I was 12 years old, and had studied
the large grains of mica in samples of granite that I had collected, and
had also observed that sheets of mica were used as windows in the
wood-burning stove in the house in which I had lived with my par-
ents and my two sisters. I read a paper that Mauguin had published
in 1927, in which he gave the dimensions a = 5.17 A, b = 8.94 A,

62 The Chemistry of Soils

c = 20.01 A, with p = 96° for the monoclinic (pseudohexagonal)
unit cell of structure of muscovite. I also made Laue photographs
and rotation photographs of a beautiful blue-green translucent spec-
imen of fuchsite, a variety of muscovite containing some chromium,
and verified Mauguin's dimensions.

The crystal of fuchsite had been given to me, along with about a
thousand other mineral specimens, in 1928, by my friend J. Robert
Oppenheimer, who had obtained them, mainly by purchase from
dealers, when he was a boy. Oppenheimer's first published paper,
written when he was about 16 years old, was in the field of miner-
alogy. He later got his bachelor's degree in chemistry from Harvard
University and then a Ph.D. in physics from Gottingen. Many of my
early X-ray studies of minerals were made with specimens from the
Oppenheimer collection, and I still take pleasure in examining some
of the more striking specimens.

I recognized at once that the layers clearly indicated to be present in
mica by the pronounced basal cleavage contained close-packed layers
of oxygen atoms, and that the dimensions were similar to octahedral
layers in hydrargillite and brucite and also tetrahedral layers in beta-
tridymite and beta-cristobalite, the dimensions for hydrargillite (now
called gibbsite) and the two forms of silica being equal to those for
the mica sheets to within about two percent. With the rules about the
structure of complex ionic crystals as a guide, the structure of mica
could at once be formulated as consisting of a layer of aluminum octa-
hedra condensed with two layers of silicon tetrahedra, one on each
side, with these triple layers superimposed with potassium ions in
between. Calculation of the intensities of the X-ray diffraction max-
ima out to the 18th order from the basal plane gave results agreeing
well with the observed intensities, so that there was little doubt that
this structure was correct for mica. I pointed out in my paper, which
was communicated to the National Academy of Sciences on January
16, 1930, and published a month later [February issue, (1930) Proc.
Nat. Acad. Sci. USA 16:123-129] that clintonite, a brittle mica, has
a similar structure, with the triple layers held together by calcium
ions instead of potassium ions, and that the correspondingly stronger
forces bring the layers closer together, the separation of adjacent lay-
ers being 9.5 to 9.6 A in place of the value of 9.9 to 10.1 A for the
micas. I also pointed out that talc and pyrophyllite have the same
structure, but with the layers electrically neutral, and held together
only by stray electrical forces. As a result these crystals are very soft,
feeling soapy to the touch, whereas to separate the layers in mica, it
is necessary to break the bonds of the univalent potassium ions, so
that the micas are not so soft, thin plates being sufficiently elastic to
straighten out after being bent, and that the separation of layers in
the brittle micas involves breaking the stronger bonds of bipositive

Soil Minerals 63

calcium ions, these minerals then being harder and brittle instead of
elastic, but still showing perfect basal cleavage. I also mentioned the
significance of the sequence of hardness in relation to the strength of
the bonds: talc and pyrophyllite, 1-2 on the Mohs hardness scale, the
micas, 2-3, and the brittle micas, 3.5—6.

I then made Laue photographs and oscillation photographs of
specimens of penninite and clinochlore, and found a monoclinic unit
of structure with a = 5.2-5.3 A, b = 9.2-9.3 A, c = 14.3-14.4 A, and
monoclinic angle of 96° 50/. It was clear from the dimensions and
the pronounced basal cleavage that the chlorites consisted of layers
somewhat similar to those found in mica. At first I tried to formulate
a single layer made of two octahedral and two tetrahedral layers, but
I soon recognized that there are layers similar to the mica layers, with,
however, layers similar to the brucite or hydrargillite layers, but with
a positive electrical charge interspersed between them, in place of the
potassium ions in mica. I then communicated a paper to the Proceed-
ings of the National Academy of Sciences on July 9, 1930, while my wife
and I and our eldest son, Linus Jr. (then five years old) were in Europe.
This paper was published two months later [Pauling, L. (1930) The
structure of chlorites. Proc. Nat. Acad. Sci. USA 16:578-582] , with the
title "The Structure of Chlorites." There was good agreement between
the calculated intensities of X-ray maxima out to the 26th order from
the basal plane and the observed intensities.

In this paper I also proposed a structure for kaolinite, consisting of
an octahedral layer with a silicon tetrahedral layer on only one side.
I also mentioned that with this unsymmetrical layer there would be
a tendency for the layer to curve, one face becoming concave and the
other convex, and that this tendency would in general not be over-
come by the relatively weak forces operated between adjacent layers.
I did not predict that jelly roll structures of clay minerals would be
found (and perhaps already had been reported at that time; I am not
sure about when they were discovered), but I used the argument that
unsymmetrical layers probably would be curved, and only in some
clay minerals, kaolinite, would the tendency to curve be overcome
by the forces between layers. I also discussed briefly the possibility
that a clay mineral similar to chlorite, but with a neutral brucite layer,
might exist, and I suggested the possibility that more complex miner-
als might be discovered, with alternation between the mica structure
and the chlorite structure.

It now seems to me to be odd that I should have published the
mica paper without mentioning talc and pyrophyllite in the title, and
the chlorite paper without mentioning kaolinite in the title. Also,
each of these papers ends with the statement that a detailed account
of the investigation would be published in the journal Zeitschrift fur
Kristallographie, and in fact no such detailed accounts were published.

64 The Chemistry of Soils

I made many more X-ray photographs of specimens of micas and
chlorites, and had my graduate student Jack Sherman make many
such photographs. This work was never completed, however, partially
because Jack Sherman soon became tired of the experimental work
and began making quantum mechanical calculations with me, and I
also became much involved during 1930 and later years in working on
the quantum mechanics of the chemical bond and on a new method
that we were starting to use in our laboratory, the determination of
the structure of gas molecules by the diffraction of electrons. It was,
of course, poor judgment on my part to say that detailed discussions
would be published later.

My first graduate student, Sterling Hendricks, after he left Pasadena,
carried out a number of investigations of the micas and the chlorites,
as well as of other minerals. Jack Sherman continued to make cal-
culations, and his X-ray studies of the micas remain his only effort
in this field (never published). I, however, together with my students
and associates, made many more studies of the crystal structure of
minerals, and I have retained my interest in this field up to the present
time. In fact, my most recent mineral paper, published together with
my son-in-law Barclay Kamb [(1982) American Mineralogist 62:817-
82 1 ] is on the crystal structure of lithiophorite, which is a clay mineral.
The structure that we assigned to lithiophorite, Ali4Li6Mn2i(OH)84,
involves alternative brucite (octahedral) layers of two kinds. One layer
has the composition Ali4Li(OH)42, with one octahedron in 2 1 vacant,
and the other layer has the composition Mn 3 Mnjg O42. The hexag-
onal unit has a = 13.37 A and c = 28.20 A, space group P3i. The
determination of this structure involved the application of structural
principles in a somewhat new way, which might be useful in the
consideration of other complex clay minerals. The new way consists
in consideration of transfer of charge through hydrogen bonds in
relation to the electroneutrality principle.

At the present time my work in X-ray and electron diffraction by
crystals relates to intermetallic compounds, especially the so-called
quasicrystals, and the structures of metals under high pressure. I may,
however, get interested in the clay minerals again, since I remember
how much excitement and pleasure I had in 1929 and early 1930 when
I was working on the micas, chlorites, and related substances.

Linus Pauling
Palo Alto, California

Soil Humus

3.1 Biomolecules

Soils are biological milieux teeming with microorganisms. Ten grams of fertile
soil may contain a population of bacteria alone exceeding the world popula-
tion of human beings, with the number of different bacterial species present
exceeding one million. One kilogram of uncontaminated soil serves as habitat
for up to 10 trillion bacteria, 10 billion actinomycetes, and one billion fungi.
Even the microfauna population (e.g., protozoa) can approach one billion in
a kilogram of soil. These microorganisms play essential roles in humification,
the transformation of plant, microbial, and animal litter into humus (Section
1.1). Humus formed in soils and sediments is the largest repository of organic
C on the planet (four times that of the biosphere), producing annual CO2
emissions through microbial respiration that are about an order of magni-
tude larger than those currently attributable to fossil fuel combustion. Clearly
the biogeochemistry of humus is of major importance to the cycling of C
and, therefore, to that of N, S, P, and most of the metal elements discussed in
Chapter 1.

Biomolecules are the compounds in humus synthesized to sustain directly
the life cycles of the soilbiomass. They are usually the products of litter degra-
dation and microbial metabolism, ranging in complexity from low-molecular
mass organic acids to extracellular enzymes. Organic acids are among the
best characterized biomolecules. Table 3.1 lists five aliphatic organic acids that
are found commonly associated with microbial activity or rhizosphere chem-
istry. These acids contain the molecular unit R-COOH, where COOH is the

66 The Chemistry of Soils

Table 3.1

Common aliphatic organic acids in soils.

Name

Chemical Formula

Formic acid HCOOH
Acetic acid CH 3 COOH
Oxalic acid HOOCCOOH
H
O

PH d

3.8
4.8
1.3

Tartaric acid HOOC— C— COOH 3.O

H I

O
H

COOH
H I H
Citric acid HOOCC — C— C COOH 3.1

H I H

a The pH value at which the most acidic carboxyl group
has a 50% probability to be dissociated in aqueous
solution.

carboxyl group and R represents H or an organic moiety such as CH3 or even
another carboxylic unit. The carboxyl group can dissociate its proton easily in
the normal range of soil pH (see the third column of Table 3.1) and so is an
example of a Bransted acid. The dissociated proton can attack soil minerals to
provoke their decomposition (see eqs. 1.2— 1.4), whereas the carboxylate anion
(COO - ) can form soluble complexes with metal cations released by mineral
weathering (see Eq. 1.4). The total concentration of organic acids in the soil
solution ranges from 0.01 to 5 mol m , which is quite large relative to trace
metal concentrations (<1 mmol m -3 ). These acids have very short lifetimes
in soil (perhaps hours), but they are produced continually throughout the life
cycles of microorganisms and plants.

Formic acid (methanoic acid), the first entry in Table 3.1, is a mono-
carboxylic acid produced by bacteria and found in the root exudate of corn.
Acetic acid (ethanoic acid) also is produced microbially — especially under
anaerobic conditions — and is found in the root exudates of grasses and herbs.
Formic and acetic acid concentrations in the soil solution range from 2 to 5
mol m -3 . Oxalic acid (ethanedioic acid), ubiquitous soils, and tartaric acid
(D-2,3-dihydroxybutanedioic acid) are dicarboxylic acids produced by fungi
and excreted by the roots of cereals; their soil solution concentrations range
from 0.05 to 1 mol m -3 . The tricarboxylic citric acid 2-hydroxypropane-
1,2,3-tricarboxylic acid also is produced by fungi and is excreted by plant

Soil Humus 67

roots. Its soil solution concentration is less than 0.05 mol m . Besides these
aliphatic organic acids, soil solutions contain aromatic acids with a funda-
mental structural unit that is a benzene ring. To this ring, carboxyl (benzene
carboxylic acids) or hydroxyl (phenolic acids) groups can be bonded in a vari-
ety of arrangements. The soil solution concentration of these acids is in the
range 0.05 to 0.3 mol m .

Organic acids with the chemical formula

H
R— C— COOH

NH 2

are amino acids. These acids, with concentration in the soil solution that is
typically in the range 0.05 to 0.6 mol m -3 , can account for as much as one half
the N in soil humus. Several of the most abundant amino acids in soils are
listed in Table 3.2. Glycine and alanine are examples of neutral amino acids, for
which the side-chain unit R contains neither the carboxyl group nor the amino
group, NH2. The name neutral is apt because the COOH group contributes a
negative charge by dissociating a proton, whereas NH2 contributes a positive
charge by accepting a proton to become NH3 . Neutral amino acids account
for about two thirds of soil amino acids. Acidic amino acids, for which R
includes a carboxyl group (aspartic and glutamic acids), and basic amino
acids, for which R includes an amino group (arginine and lysine), account for
about equal portions of the remaining one third. Amino acids can combine
according to the reaction

H H

R— C— COOH + R'— C— COOH

NH 2 NH 2

H O R
— > R— C — C— N — CH — COOH + H 2 (3.1)

NH 2 H

to form a peptide,

R'
H O I

R— C— C— N— CH
NH 2 H

the fundamental repeating unit in proteins. Because the peptide group is
repeated, proteins are polymers, and because water is a product in pep-
tide formation (Eq. 3.1), proteins are specifically condensation polymers of
amino acids. Peptides of varying composition and structure are the dominant
chemical form of amino acids in soils.

68 The Chemistry of Soils

Table 3.2

Common amino acids in soils.

Name

Glycine

Alanine

Chemical formula

NH 2

I
HC— COOH

NH 2

I
CH 3 — C — COOH
H

NH 2

Aspartic acid HOOC — CH 2 — CH — COOH

NH 2

Glutamic acid HOOC— CH 2 — CH 2 — C— COOH

Arginine

NH 2 — C — NH — CH 2 — CH 2 — CH 2

NH 2

I
CH — COOH

Lysine

NH 7

NH 2 — CH 2 — CH 2 — CH 2 — CH 2 — CH — COOH

Another class of important and highly specialized biomolecule is rep-
resented by the siderophores, which are low-molecular mass compounds
synthesized by bacteria, fungi, and grasses to scavenge and compete for Fe(III)
in minerals and other sources of nutrient Fe under oxic, Fe-limited con-
ditions. Nearly 500 different siderophore compounds have been identified
and characterized. Microbial siderophores complex Fe(III) with hydroxa-
mate, catecholate, and hydroxycarboxylate functional groups. Hydroxamate
(HO — N — C=0) groups are found mainly in siderophores produced by
fungi, actinomycetes, and some bacteria, whereas catecholate (aromatic acid
with two adjacent OH on the benzene ring) and hydroxycarboxylate (HO —
C-COOH) groups are found mainly in siderophores produced by certain
bacteria (notably, pseudomonads) and by fungi. The concentrations of these
siderophores in the soil solution are estimated to be in the nanomolar range.
Almost all siderophores contain three complexing functional groups that bind
Fe 3+ in octahedral coordination with O ligands. These functional groups
typically are located along a relatively long molecular chain that constitutes

Soil Humus 69

the siderophore "backbone" and thus can act more or less independently as
they form complexes of remarkably high stability. Siderophores are known
to complex both bivalent metal cations and trivalent metal cations besides
Fe 3+ — particularly, Al 3+ , Co 3+ , and Mn 3+ . These additional complexes are
believed to play roles in reducing metal toxicity to microorganisms as well as
in facilitating their uptake of metals.

Carbohydrates, biopolymers of plant and microbial origin that can
account for up to one half of the organic C in soil humus, include the monosac-
charides listed in Figure 3.1. The monosaccharides have a ring structure with
a characteristic substituent group and arrangement of hydroxyls. In glucose,
galactose, and mannose, the substituent group is CH2OH, whereas in xylose
it is H, in glucuronic acid it is COOH, and in glucosamine it is NH2. (Note
the close structural relationship among glucose, glucuronic acid, and glu-
cosamine in Fig. 3.1.) Xylose is a monosaccharide of plant origin, whereas
galactose, mannose, and glucosamine are of microbial origin. Glucose and the
other monosaccharides in Figure 3.1 are rapidly metabolized by microorgan-
isms in soil. However, monosaccharides polymerize to form polysaccharides.
For example, two glucose units can link together through oxygen at the site of
HOH in each to form a repeating unit of cellulose after eliminating water. Thus
cellulose, the major carbohydrate found in plants, is a condensation polymer
of glucose. It can account for up to one sixth of the organic C in soil.

Glucose

CH 2 OH

O. OH

CH 2 OH

HO
Galactose k qH

O OH

COOH

O OH

Glucuronic acid KoH
HO

Mannose

A OH

CH 2 OH

O OH

Glucosamine K^H

NH„

Xylose

HC \\ O^ OH

.OH

Figure 3.1. Common monosaccharides in soils.

70 The Chemistry of Soils

The biomolecules just described are among the most abundant in soils,
but by no means do they exhaust the long list of organic compounds pro-
duced by living organisms in the soil environment. Organic P compounds,
which can account for up to 80% of soil P, occur principally in the form of
inositol phosphates (benzene rings with H2PO4 bound through O to the ring
carbon atoms), and organic S compounds, which can account for nearly all the
soil S, occur principally as S-containing amino and phenolic acids and polysac-
charides. The chemistry of biomolecules of low relative molecular mass, such
as siderophores and those listed in Tables 3.1 and 3.2, has a strong influence
on acid— base and metal complexation reactions in soils, whereas the chem-
istry of biopolymers such as polysaccharides influences the surface and colloid
chemistry of soils through adsorption reactions with the solid particles in soil.

3.2 Humic Substances

In simple terms, humic substances are organic compounds in humus not syn-
thesized directly to sustain the life cycles of the soil biomass (Section 1.3).
More specifically, they are dark-colored, biologically refractory, heterogeneous
organic compounds produced as by-products of microbial metabolism. They
may account for up to 80% of soil humus (and up to half of aquatic humus),
and differ from the biomolecules present in humus because of their long-term
persistence (see Problem 3 in Chapter 1) and their molecular architecture.
This broad concept of humic substances implies neither a particular pathway
of formation and resulting set of organic compounds, nor a characteristic
relative molecular mass and associated chemical reactivity. However, it does
exclude exogenous materials such as kerogen, a complex hydrocarbon mix-
ture that constitutes nearly all the organic matter in sedimentary rocks, and
black carbon, an equally complex mixture of organic compounds produced
by combustion processes, including fossil fuel burning and fire. These two
organic mixtures typically enter soils from parent material and atmospheric
deposition respectively.

The chemical properties of humic substances are often investigated after
fractionation of soil humus based on solubility characteristics. Organic mate-
rial that has been solubilized by mixing soil with a 500 mol m NaOH solution
is separated from the insoluble material (termed humin) and brought to pH 1
with concentrated HCl. The precipitate that forms after this acidification is
called humic acid, whereas the remaining, soluble organic material is called
fulvic acid. Repeated extractions of this type are often done on the humin and
humic acid fractions to enhance separation. The humic and fulvic acids recov-
ered also are subjected to centrifugation and ion exchange resin treatments to
remove inorganic constituents and loosely associated biomolecules.

The average chemical composition of soil humic and fulvic acids world-
wide is summarized in Table 3.3. Except for the content of S (for which the
number of available measurements is about one third the number available for

Soil Humus 71

Table 3.3

Mean content (measured in grams per kilogram) of nonmetal elements in soil
humic substances worldwide. 3

Substance C H N S O H/C O/C

Humic acid 554 ± 38 48 ± 10 36 ± 13 8 ± 6 360 ± 37 1.04 ± 0.25 0.50 ± 0.09
Fulvic acid 453 ± 54 50 ± 10 26 ± 13 13 ± 11 462 ± 52 1.35 ± 0.34 0.78 ± 0.16

a Rice, J. A., and P. MacCarthy. (1991) Statistical evaluation of the elemental composition of
humic substances. Org. Geochem. 17:635.

the other elements), these data do not differ greatly from the average chem-
ical composition of aquatic humic and fulvic acids or those extracted from
peat deposits. Overall the remarkably small standard deviations around the
mean values listed in Table 3.3 suggest that humification processes in soil yield
characteristic refractory organic products in the two fractions, irrespective
of environmental conditions. The average chemical formulas for humic and
fulvic acid given in Section 1.3 were developed from the composition data
in Table 3.3 (see Problem 7 in Chapter 1). On the basis of a formula unit
containing 1 mol H, for which there is no statistically significant difference
in content between the two fractions, the average relative molecular mass of
humic acid would be larger than that of fulvic acid. Detailed statistical analyses
indicate that there is more C and N but less O per unit mass in humic acid
compared with fulvic acid. Thus the molar ratios H-to-C and O-to-C both
are larger in fulvic acid than they are in humic acid, implying that the latter
is the more aromatic (see Section 1.3) and less polar humic substance. Non-
invasive spectroscopic methods have proved useful in obtaining a fingerprint
of the distribution of C in the two fractions, which supports these infer-
ences. On average, about half the C in soil fulvic acids is associated with polar
O-containing moieties, whereas a quarter of the C is associated with aromatic
moieties. For humic acids, on the other hand, about one third of the C is
aromatic, whereas polar C accounts for about 40% of the total.

Careful spectroscopic examination of humic substances in aqueous solu-
tion, after treatment with organic acids and solvents to provoke disaggregation,
indicates that humic and fulvic acids are in fact assemblies (supramolecular
associations) of many diverse components having rather low relative molecu-
lar masses (< 2000 Da). These components appear to be held together mainly
by hydrogen bonds and hydrophobic interactions (Section 3.4). Thus, the
average relative molecular mass of humic substances, particularly humic acid,
characterizes a supramolecular association, not a polymer in the sense of the
protein and carbohydrate structures discussed in Section 3.1. Fulvic acid, with
its more polar nature, is less likely than humic acid to engage in hydrophobic
interactions and thus may be pictured in aqueous solution more simply as a
dynamic mixture of molecularly small polar components with an association
that is largely unaffected by pH, consistent with its defining solubility property.

72 The Chemistry of Soils

In keeping with these observations, the carboxyl content of humic acids
tends to range from 3 to 5 mol kg , whereas that for fulvic acids ranges from
4 to 8 mol kg -1 . The phenolic OH content of both humic and fulvic acids
ranges from 1 to 4 mol kg -1 . These two classes of functional group provide
essentially all the Bransted acidity of humic substances, which, as indicated by
their ranges of carboxyl content, is significantly larger for fulvic acids than it
is for humic acids. Because most of this acidity is reactive below pH 7 (Table
3.1), and protonation of their amino groups is limited, humic substances bear
a net negative charge in all but the most acidic soils. Besides these impor-
tant O-containing functional groups, a variety of moieties derived from the
microbial degradation of biopolymers are found in humic substances. These
moieties include fragments of polysaccharides (which are also O containing
and account for up to one fourth of the C in humic substances), peptides [the
principal chemical form of N in humic substances, also O containing, and
characterized by the amide group (HN — C= O)], lipids (organic molecules
of relatively low water solubility with mixed hydrophilic-hydrophobic char-
acter), and lignin (a polymer comprising aromatic alcohols that feature a
three-C chain attached to a benzene ring). Alkyl moieties in humic substances,
which account for about one fourth of their total C, may be contributed by
many of these biopolymeric fragments. They tend to increase in importance
with increasing molecular mass and to become associated with hydrophobic
domains.

Thus, humic substances emerge from a slow process of biological decom-
position, oxidation, and condensation as characteristic organic mixtures
having two fundamental properties:

1. Supramolecular association: self-organized assemblies of diverse
low-molecular mass organic compounds that have either a
predominantly hydrophilic (fulvic acid) or hydrophilic-hydrophobic
(humic acid) nature, with the latter being mediated in aqueous solution
by hydrogen bonds and hydrophobic interactions.

2. Biomolecular provenance: identifiable biopolymeric fragments that form
an integral part of a labile molecular architecture and that govern both
conformational behavior and chemical reactivity.

3.3 Cation Exchange Reactions

Soil humus plays a major role in the buffering of both proton and metal
cation concentrations in the soil solution. The mechanistic basis for this buffer
capacity is cation exchange. A cation exchange reaction involving dissociable
protons in soil humus and a cation like Ca + in the soil solution can be
written as

SH 2 (s) + Ca 2+ = SCa(s) + 2H+ (3.2)

Soil Humus 73

where SH2 represents an amount of particulate humus (S) bearing 2 mol
dissociable protons, and SCa is the same amount of humus bearing 1 mol
exchangeable Ca 2+ . The symbol S 2_ then would represent an amount of par-
ticulate humus bearing 2 mol negative charge that can be neutralized by cations
drawn from the soil solution.

The prospect of interpreting S in Eq. 3.2 at the level of detail typi-
cal for minerals or biopolymers is dimmed by the need to consider, in the
case of humus, many competing cation exchange reactions involving charged
organic fragments. Even if the molecular architecture of each possible cation-
humus association were worked out, the use of Eq. 3.2 for them would
entail the determination of a large number of chemical parameters — too
many for the set of data usually available from a cation exchange experi-
ment to provide. For this reason, and because of the complicated way the
structural characteristics described in sections 3.1 and 3.2 influence humus
reactivity, the modeling of cation exchange reactions involving soil humus
always interprets Eq. 3.2 in some average sense. This perspective is empha-
sized by expressing the H + — Ca + cation exchange reaction in an alternate
form:

2=SOH(s) + Ca 2+ = (=SO) 2 Ca(s) + 2H+ (3.3)

In this case, =SOH represents an amount of acidic functional groups in
humus bearing 1 mol dissociable protons, and (=SO)2Ca is twice this
amount. Equations 3.2 and 3.3 are equivalent ways to represent the same
cation exchange process, and neither has any particular structural impli-
cation. Equations 3.2 and 3.3 do not imply, for example, that a "humus
anion" exists with either the valence —1 or —2. The choice of which
equation to use is a matter of personal preference, because both satisfy
general requirements of mass and charge balance (see Special Topic 1 in
Chapter 1).

The cation exchange capacity (CEC) of soil humus is the maximum num-
ber of moles of proton charge dissociable from unit mass of solid-phase
humus under given conditions of temperature, pressure, and aqueous solution
composition, including the humus concentration. A method widely used to
measure CEC for humus involves determining the moles of protons exchanged
in the reaction

2=SOH(s) + Ba 2+ = (=SO) 2 Ba(s) + 2H+ (3.4)

where the Ba 2+ ions are supplied in a 100 mol m -3 Ba(OH)2 or BaCi2 solution
at a selected pH value. Measurements of this kind indicate that the CEC of
humic acids ranges typically between 5 and 9 mol c kg , whereas for peat
materials it ranges from 1 to 4 mol c kg . The CEC range observed for humic
acids is consistent with the ranges of carboxyl and phenolic OH content given
in Section 3.2.

74 The Chemistry of Soils

300

200

100

I SH^S 2 Ca

_,-—

- ^^q*-* > "'^

/ S 2 Ca^SH
/ H + - Ca 2+ Exchange

_ i — 1_

60
Time (s)

100

Figure 3.2. Graphs of the moles of adsorbed Ca charge versus time for the cation
exchange reaction in Eq. 3.4 with Ca + as the metal cation replacing H + on a sphagnum
peat. Filled circles depict the forward (left to right) direction, whereas open circles
depict the backward (right to left) direction. Data from Bunzl, K., et al. (1976) Kinetics
of ion exchange in soil organic matter. IV. /. Soil Sci. 27:32.

The kinetics of H + -Ca 2+ exchange are illustrated in Figure 3.2
for a suspension of sphagnum peat. The data show the time develop-
ment of the formation of (=SO)2Ca (filled circles) after the addition of
50 |xmol Ca 2+ charge and the depletion of (=SO)2Ca (open circles) after
the addition of 50 ixmol H + charge to a suspension containing 0. 1 g peat. It is
apparent that the exchange process is relatively rapid. Note that the reaction in
Eq. 3.3 proceeds from left to right more readily than from right to left, starting
from comparable initial conditions. Additional experiments and data analysis
showed that the approximately exponential time dependence of the graphs in
Fig. 3.2 can be described by a film diffusion mechanism. The basic concept of
this mechanism is that the rate of cation exchange is controlled by diffusion of
the exchanging ions through a thin (2—50 jxm) immobile film of solution sur-
rounding a humus particle in suspension. Film diffusion, discussed in Special
Topic 3 at the end of this chapter, is a common process invoked to interpret
the observed rates of cation exchange on soil particles.

When the metal cation replacing a proton on soil humus is monovalent
and Class A, with low IP (Section 1.2), it is often considered a background
electrolyte ion in the analysis of proton exchange data. This is done on the
hypothesis that all such monovalent metal cations have a much lower affinity
for humus than the proton. Attention is then focused on the species =SOH.
Experimental measurements of the number of moles of strong acid or strong
base added to a suspension (or solution) of humus to provoke cation exchange
are combined with pH measurements (a combination termed a titration) to

Soil Humus 75

calculate the apparent net proton charge:

(n A -[H+]v)-(n B -[OH-]v)

OCTH.titr = (3. 5 J

where riA is the number of moles of strong acid (like HCl) added, and n B is the
number of moles of strong base (like NaOH) added to bring a suspension (or
solution) to the volume V with a "free" aqueous proton concentration equal
to [H + ] moles per unit volume. The concentration of [H + ] can be deter-
mined through a pH measurement, as can that of [OH - ]. (Usually, [OH - ]
~ 10 -14 /[H + ] in dilute solutions, if concentrations are in moles per cubic
decimeter.) The numerator in Eq. 3.5 is the difference between H + bound and
OH - bound by the humus sample, with bound calculated as the difference
between moles of added ion and moles of free ion. (Note that bound OH - is
equivalent to dissociated H + .) After division by m s , the dry mass of humus,
one has computed the apparent net proton charge. To convert this quantity to
the true net proton charge, an, two steps must be taken. First, corrections must
be made for unwanted side reactions involving the added protons or hydroxide
ions. These include the formation or dissociation of proton complexes (e.g.,
HCO^~ formed from C0 3 - or the reverse reaction, see Problem 15 in Chapter
1) and the dissolution of any minerals present by protonation (Section 1.5) or
hydroxide reaction, because none of these reactions involves humus. If only
the first type of reaction is occurring, it can be taken into account by a blank
titration of an aliquot of the aqueous solution contacting the humus sample
obtained by separation prior to the addition of strong acid or base. An appar-
ent net proton charge is calculated for this solution using Eq. 3.5 and is then
subtracted from <5aH,titr f° r tne humus suspension (or solution). If mineral
dissolution reactions do occur during a titration of humus, they must be taken
into account through careful monitoring of the soluble dissolution products
(e.g., Al 3+ ) and consideration of both the protonation of the mineral leading
to dissolution and the reactions of the soluble dissolution products (e.g., the
hydrolysis of Al , which produces free protons).

The second step required to convert an apparent net proton charge to CTh is
the establishment of a datum for the blank-corrected 5an,titr at some pH value.
This must be done because the apparent net proton charge is, by definition,
measured relative to its initial unknown value in the humus suspension (or
solution) prior to the addition of strong acid or base. If 5an,titr exhibits a
well-defined plateau at low pH, corresponding to the complete protonation
of all acidic functional groups, this plateau value can be taken as a datum to
be subtracted from all measured values of 5an,titr to obtain an, which then
will approach zero as pH decreases to the value at which the plateau begins.
Alternatively, if the content of carboxyl plus phenolic OH groups has been
measured directly, and if it is assumed that only these two acidic functional
groups contribute to an, then their combined content may be subtracted from
the apparent net proton charge to obtain a true value. In this case, the datum

76 The Chemistry of Soils

occurs at the pH value where <5cfH,titr i s equal and opposite to the combined
content of carboxyl and phenolic OH groups. These two examples illustrate
the point that the conversion of a blank-corrected <5ffH,titr to obtain CTh can be
problematic.

Figure 3.3 shows a graph of a blank-corrected 5an,titr versus -log[H + ]
based on the base titration of a purified humic acid extracted from peat.
Potassium hydroxide was added incrementally to increase pH and produce
the exchange reaction

eSOK + H+ = =SOH + K+

(3.6)

The pH values measured were converted to -log[H + ] in the KNO3 solutions
used as a background electrolyte, where [H + ] is in moles per cubic decimeter
(liter). Equation 3.5 was used to compute 5an,titr at each value of-log[H + ],
after which blank titration corrections were performed. The graph in Figure 3 .3
thus depicts the blank-corrected apparent net proton charge of the humic acid
sample at several ionic strengths.

Three characteristic features of the net proton charge on humus are evi-
dent in Figure 3.3: (1) negative values over a broad range of pH; (2) the
absence of well-defined plateaus, inflection points, or other signatures of dif-
ferent classes of acidic functional group as observed typically in the titration
curves of well-defined organic acids; and (3) a tendency to become more nega-
tive in value with increasing concentration of the background electrolyte. The
first-named property indicates a dominant contribution of proton dissocia-
tion over the normal range of pH in soils, whereas Property 2 implies that the

2 -3

~~ I 1 1 1 1 1 1 —

Peat Humic Acid jX

6 7 8
- log [H + ]

Figure 3.3. Graph of the apparent net proton charge on a peat humic acid versus
-log[H + ] at several ionic strengths. Reprinted with permission from Kinniburgh,
D. G.,etal. (1996) Metal ion binding by humic acid: Application of the NICA-Donnan
model. Environ. Sci. Technol. 30:1687-1698.

Soil Humus 77

acidic functional groups present in humus dissociate protons in overlapping
ranges of pH, as opposed to exhibiting widely separated characteristic pH val-
ues for proton dissociation. Property 3 is consistent with the cation exchange
reaction in Eq. 3.6 being driven to the left as the concentration of K + increases.
Note that the change in net proton charge between pH 3 and 10 is larger than
the maximum structural charge observed in 2:1 clay minerals and Mn oxides
(Sections 2.3 and 2.4). Changes twice as large as this are observed in similar
titration measurements for solutions of fulvic acid.

The acid-neutralizing capacity (ANC) of humus in suspension or solution
is equal to the concentration of its dissociated acidic functional groups:

ANC=-a H c s (a H <0) (3.7)

where c s is the humus concentration in kilograms per cubic decimeter. Clearly,
ANC will increase from zero, at some low value of pH, to the CEC of humus,
expressed as a concentration in moles per cubic decimeter (liter), at high
pH. The change in ANC with pH (strictly, the derivative dANC/dpH) is
called the buffer intensity, Ph- If the ANC increases greatly as pH increases,
then the solution constituents have a large increase in their capacity to bind
and thus neutralize protons; this corresponds to a large buffer intensity. Speak-
ing generally, one can estimate the buffer intensity to be greatest when Ch
changes most rapidly with -log[H + ]. In Figure 3.3, this occurs in the range
4 < — log[H + ] < 6, which is typical for soil humus materials. (Note that Ph
does not depend on the datum selected for an.) It is for this reason that soil
humus is so important in the buffering of acidic soils.

3.4 Reactions with Organic Molecules

The organic compounds that react with soil humus are derived from pesti-
cides, pharmaceuticals, industrial wastes, fertilizers, green manures, and their
degradation products. Humus in solid form, either as a colloid or as a coating
on mineral surfaces, can immobilize these compounds by adsorption and, in
some instances, detoxify or deactivate them. Soluble humus, typically the ful-
vic acid fraction, can form complexes with organic compounds that then may
travel freely with percolating water into the soil profile. Toxic organic materials
that otherwise might be localized near the land surface can be transported by
this mechanism. Similar transport may occur for organic molecules adsorbed
by mobilized humus colloids.

Soil humus reacts by cation exchange with organic molecules that contain
N atoms bearing a positive charge. These kinds of structures occur in both
aliphatic and aromatic compounds, the latter being common in pesticide and
pharmaceutical preparations. The general reaction scheme is analogous to
Eq. 3.6:

+
=SOH(s) + R-N ==SON-R(s) + H+ (3.8)

78 The Chemistry of Soils

where R represents an organic unit bonded to the N atom. Spectroscopic
studies of this reaction indicate that some electron transfer from humus to
the N compound takes place, thereby enhancing the stability of the humus-
organic complex. Humus also contains electron-deficient aromatic moieties,
such as quinones or other benzene rings with highly polar substituents, that can
attract and bind electron-rich molecules, such as polycyclic aromatic hydro-
carbons (PAH; two or more fused benzene rings), to form stable charge-transfer
complexes.

Organic molecules that become positively charged when protonated can
react with COOH groups in soil humus by proton transfer from the latter to
the former. Basic amino acids, like arginine (Table 3.2), with two "protonat-
able"NH2 groups, are good examples of these compounds, as are the s-triazine
herbicides, which contain protonatable N substituents on an aromatic ring.
Protonated functional groups like COOH and NH also can form hydrogen
bonds with electronegative atoms such as O, N, and F. As an example, the
C = O group in the phenylcarbamate and substituted urea pesticides can form
a hydrogen bond (denoted . . .) with NH in soil organic matter, C = O . . . HN,
and NH groups in the imidazolinone herbicides can form hydrogen bonds
with C = O groups in humus. (Hydrogen bonds of this type also form in
peptides.) Humus contains carboxyl, hydroxyl, carbonyl, and amino groups in
a broad variety of molecular environments that lead to a spectrum of possibil-
ities for hydrogen bonding within its own supramolecular structure and with
exogenous organic compounds. The additive effect of these interactions makes
hydrogen bonding an important reaction mechanism, despite its relatively low
bonding energy.

Much of the supramolecular architecture of soil humus is not electri-
cally charged. This nonionic structure can nevertheless react strongly with
the uncharged part of an organic molecule through van der Waals interac-
tions. The van der Waals interaction involves weak bonding between polar
units, which may be either permanent (like OH and C = 0) or induced
momentarily by the presence of a neighboring molecule. The induced van
der Waals interaction is the result of correlations between fluctuating polar-
ization created in the "electron clouds" of two nonpolar molecules that
approach one another closely. Although the average polarization induced in
each molecule by the other is zero (otherwise they would not be nonpolar
molecules), the negative correlations between the two induced polariza-
tions do not average to zero. These correlations produce a net attractive
interaction between the two molecules at very small distances (around
0.1 nm). The van der Waals interaction between two molecules is very weak,
but when many molecules in a supramolecular structure like humus inter-
act simultaneously, the van der Waals component is additive and, therefore,
strong.

The interaction between uncharged molecules (or uncharged portions of
molecules) and soil humus is often stronger than the interaction between
these kinds of molecules and soil water, resulting in their exit from the

Soil Humus 79

soil solution to become adsorbed by humus. This occurs for two distinct
reasons. First, water molecules interacting with a nonpolar molecule in the
soil solution are confronted by a lack of electronegative atoms with which
to form a hydrogen bond, so they cannot orient their very polar OH toward
the molecule in ways that are compatible with the tetrahedral coordination
they engage in the bulk liquid structure. Instead, the water molecules must
form a network of hydrogen bonds that point roughly parallel to the surface
of the nonpolar molecule, thereby enclosing it in a kind of cage structure
(hydrophobic effect). The resultant disruption of the tetrahedral ordering in
liquid water and the cost in energy to produce the anomalous cage result
in a low water solubility of the nonpolar molecule. The second reason for
a stronger interaction with humus is the presence of nonpolar moieties in
the latter. From the perspective of minimizing disruption of the normal liq-
uid water structure, it is optimal to have a nonpolar molecule adsorb on a
nonpolar domain of humus, so that fewer water molecules are needed to
accommodate to the two than when they are far apart. Although van der
Waals interactions between nonpolar molecules are approximately of the
same strength as those between water molecules, or those between non-
polar molecules and water molecules, the gain to the latter in not having
to form as extensive a cage structure produces a strong tendency for non-
polar units to bind together in the presence of liquid water (hydrophobic
interaction).

The relationship between the hydrophobic effect and water solubil-
ity can be quantified by two important properties of uncharged organic
molecules: the number of chlorine substituents (Nq) and the solvent-excluding
area (SES). Chlorine is a highly electronegative atom that, upon replac-
ing H on a carbon atom, can then withdraw significant electron charge
density carbon-carbon bonds in chain or ring structures, thus rendering
them less polar and more hydrophobic. Solvent-excluding area (the same
as the total surface area for a nonpolar molecule) provides a measure of
the size of the interface across which no hydrogen bonds cross, which is
created when the hydrophobic effect occurs. This interface disrupts the struc-
ture of liquid water, leading to cage formation that is inimical to high
water solubility. These ideas are summarized qualitatively in Figure 3.4,
which gives ranges of water solubility observed for several classes of tox-
icologically important organic compounds. Solubility is seen to decrease
as either the number of Cl or molecular size increases across a given
class.

Statistical correlations have been worked out that express these trends in
quantitative form and serve as useful predictors. For example, the common
logarithm of water solubility [S, expressed in moles per cubic decimeter (liter) ]
for chlorinated benzenes has been shown to decrease linearly with Nq:

log S = -0.6608 N c i - 1.7203 (R 2 = 0.98) (3.9a)

80 The Chemistry of Soils

Halogenated

C 1 and C 2 compounds

t 1 1 1 r

CCI 2 =CCI 2 CH 2 CI 2

Alkylated
benzenes

Chlorinated
benzenes

CLS-ci
ci^ci

CI "

(°T~ @

Polychlorinated C 'J IC '? 1
biphenyls CI-@— @-CI ®-^o)

CI CI CI ci

o
I

Phthalate
esters

Jl°X.°-

Polycylic aromatic ©3
hydrocarbons "" "~~

(eXc:8X <°££:

Aliphatic
hydrocarbons

C 18 H 3

C 5 H 12

1(T

10'"

10" s

10" f

10"

10-

S (mol dm"'

Figure 3.4. Ranges of water solubility for classes of organic compounds of varying
hydrophobicity produced by increasing chlorine substitution or solvent-excluding area.
Data and format from Schwarzenbach, R. P., P. M. Gschwend, and D. M. Imboden.
(2003) Environmental organic chemistry. John Wiley, Hoboken, NJ.

and that for polycyclic aromatic hydrocarbons has been shown to decrease
linearly with SES:

logS

-4.27SES + 3.07 (R z = 0.998)

(3.9b)

where SES is expressed in square nanometers. Taking as a simple — but
telling — case, the benzene molecule, with a measured log water solubility (in
the units of S presented earlier) at 25 °C is —1.64. Equation 3.9a yields —1.72
(withNci = 0), whereas Eq. 3.9b yields —1.63 using SES equal to the total sur-
face area of the benzene molecule, 1.1 nm . Both of these solubility estimates
are in agreement with the measured value.

The relationship between the hydrophobic interaction and water solubility
is often described quantitatively by a linear partition equation analogous to

Soil Humus 81

Henry's law (Section 1.4), with soil humus instead of air playing the role of
the nonaqueous phase:

K oc = ^^ (3.10)

[A(aq)]

where n is the number of moles of an organic compound A that is adsorbed
by 1 kg soil with an organic carbon content that is equal to f oc (measured
in kilograms organic C per kilogram), thus making the quantity n/f oc the
number of moles of A adsorbed per kilogram of soil organic C. The constant
parameter K oc may be termed the Chiou distribution coefficient, with units of
liters per kilogram of organic C. By hypothesis, this parameter is not dependent
(or very weakly dependent) on the chemical properties of soil humus (i.e.,
division by f oc on the right side of Eq. 3.10 is hypothesized to remove all such
dependence by normalizing n to the content of organic C in a soil). Perhaps
remarkably, this hypothesis has been verified rather well (i.e., K oc calculated
with Eq. 3.10 varying within a factor of about two) in careful studies involving a
variety of soils interacting with a single hydrophobic organic compound, such
as dichlorobenzene or carbon tetrachloride, making the Chiou distribution
coefficient a very useful model parameter.

Equation 3.10 describes the partitioning of compound A between two
phases: soil humus and the soil solution. This partitioning, in the case of
organic compounds like those shown in Figure 3.4, is expected to favor soil
humus because of the hydrophobic effect. Because the latter is inversely related
to water solubility, it is reasonable to expect that the Chiou distribution
coefficient also will be inversely related to water solubility. Such a statisti-
cal correlation often has been observed and is of the general mathematical
form

logK oc = a-blogS (3.11)

where a and b are empirical parameters that in principle depend on the class
of organic compounds under consideration. One useful correlation that holds
for a broad variety of organic compounds and predicts the value of log K oc
within ±0.45 (i.e., predicts K oc values within a factor of about three) has a =
3.95 and b = 0.62, with K oc in units of cubic decimeter (liter) per kilogram
and S in units of grams per cubic meter. For example, the industrial pollutant
1,4-dichlorobenzene has a water solubility of 83 gm -3 and, therefore, Eq. 3.11
predicts

logK oc = 3.95 -0.62 log 83 = 2.76 (3.12)

compared with an observed value of 2.74 (i.e., K oc = 550 L kg~ c ). By com-
parison, benzene has the much larger water solubility of 1780 g m (note the
dramatic effect of the chlorine substituents!), corresponding to logK oc = 1.93,
using Eq. 3.11 with the values of a and b given earlier. This is also the observed

82 The Chemistry of Soils

value, equivalent to K oc = 85 L kg~ c . Increasing water solubility corresponds
to decreasing partitioning of nonpolar compounds into soil humus. The Chiou
distribution coefficient is a quantitative parameter that captures this trend
accurately.

3.5 Reactions with Soil Minerals

Soil humus in itself is not biologically refractory. Laboratory experiments with
fungi, bacteria, enzymes, and chemical oxidants indicate clearly that humus
in aqueous extracts — even its aromatic components — can be degraded readily
under aerobic conditions over periods of days to weeks. Evidently anaerobic
conditions and, more significantly, interactions with soil particles are essential
in protecting humus from microbial attack and conversion to CO2. Numerous
circumstantial studies of the biodegradability of humus in temperate-zone
soils support this idea, with reports of organic C content and mean age of
humus increasing with decreasing particle size. Soil humus found in silt-size
particles tends to have C-to-N ratios well above the average soil value of 8
(Section 1.1), whereas that in clay-size particles does conform to the aver-
age value, indicating that protection mechanisms must be operating in the
latter that are either not available or not effective in the former. Encapsu-
lation and, therefore, physical isolation along with the attendant anaerobic
conditions likely is the principal mechanism by which humus survives in
soil silt fractions, whereas this mechanism plus strong adsorption reactions
with minerals likely contribute to the long life of humus observed for soil
clay fractions. Modulating these trends is the spectrum of inherent differing
susceptibility to microbial degradation of the components of humus them-
selves, with biopolymer fragments placed at the high end of the spectrum, alkyl
O-containing moieties placed in the middle of the spectrum, and hydrophobic
moieties placed at the low end.

The low C-to-N ratio of soil clay fractions suggests that peptidic moieties
are involved importantly in reactions of humus with soil minerals having very
small particle size. These moieties may engage in cation exchange with acidic
surface OH groups (Eq. 3.8, with the reactant=SOH now interpreted as a
mineral surface OH) or they may bind through proton transfer, hydrogen
bonding, and van der Waals interaction mechanisms, as described in Section
3.4, but with humus moieties now being the "organic molecule" and a soil
mineral being the adsorbing solid phase. The latter two modes of interaction
also apply to the other components of humus, and in particular to humic
substances.

Another important reaction mechanism that extends to any humus com-
ponent of suitable composition is bridging complexation, in which anionic
or polar functional groups (e.g., carboxylates or carbonyls) become bound
to a metal cation adsorbed by a negatively charged mineral surface (e.g.,
negative structural charge on clay minerals and Mn oxides or ionized

Soil Humus 83

surface OH). If one or more water molecules is superposed between the
adsorbed cation and the polar organic functional group, the mechanism is
termed outer-sphere bridging complexation (Fig. 3.5, also termed water bridg-
ing), whereas if the adsorbed cation is bound directly to the polar organic
functional group, it is termed inner-sphere bridging complexation (Fig. 3.6, also
termed cation bridging). As a rule, monovalent adsorbed cations form outer-
sphere bridging complexes with polar functional groups, whereas bivalent
adsorbed cations tend to form both types of complex, although Class B metal
cations (Section 1.2) are likely to form inner-sphere complexes exclusively. Of
the six modes of interaction described, the weakest are cation exchange, proton
transfer, and outer-sphere bridging complexation; the strongest are hydrogen
bonding, van der Waals interactions, and inner-sphere bridging complexation.
For humic substances, van der Waals interactions and, in particular, hydropho-
bic interactions with the atoms in a mineral surface can be quite strong and
relatively long range, resulting in the formation of very stable complexes. These
latter interaction mechanisms are especially apparent when the binding humus
moieties are large molecular fragments or when chemical conditions are such
that they suppress the ionization of acidic functional groups either in humus
or on the mineral surface — for example, when the pH value results in no net
surface charge on the latter (sections 2.3 and 2.4).

Studies of soil humus retention and recalcitrance (the latter being indi-
cated by resistance to chemical oxidants) consistently show that these two
properties are positively correlated with the content of poorly crystalline Al

Figure 3.5. Outer-sphere bridging complexation of a cation adsorbed on a clay min-
eral surface by a carbonyl group in humus, with the cation— carbonyl O distance shown
in Angstroms. Visualization courtesy of Dr. Rebecca Sutton.

84 The Chemistry of Soils

Figure 3.6. Inner-sphere bridging complexation of a cation adsorbed on a clay
mineral surface by carboxyl groups in humus, with cation-O distances shown in
Angstroms. Visualization courtesy of Dr. Rebecca Sutton.

and Fe oxyhydroxides (conventionally estimated by an extraction with ammo-
nium oxalate). A similar correlation is found for allophanic minerals, which
are inherently poorly crystalline. This relationship is an expected result of the
relatively large specific surface area of poorly crystalline metal oxyhydroxides
and aluminosilicates, which allows greater adsorption of humus per unit mass
of solid phase, and the abundance of acidic surface OH groups on these min-
erals (sections 2.3 and 2.4), which promotes greater reactivity per unit mass
of solid phase.

A mechanistic basis for the relationship is provided by ligand exchange,
a chemical reaction in which direct bond formation takes place between an
O-containing functional group in humus, typically carboxylate, and either
Al(III) or Fe(III) at the surface of a poorly crystalline Al or Fe aluminosilicate
or oxyhydroxide mineral. This reaction involves stronger chemical bonds than
those that occur even in the inner-sphere bridging complexation reaction
because the metal ion involved is part of the mineral structure, not an adsorbed
species. The general reaction scheme for ligand exchange can be expressed by
two chemical equations:

=MOH(s) + H + = =MOH+(s) (3.13a)

=MOH+(s) + S - COO" = =MOOC - S(s) + H 2 0(£) (3.13b)

Soil Humus 85

where, by analogy with Eq. 3.3, =MOH(s) represents 1 mol reactive surface
OH bound to a metal M (M = Al or Fe) in an aluminosilicate or oxyhydroxide
mineral structure and, similarly to the first reactant in Eq. 3.2, S-COO -
represents an amount of dissolved humus bearing 1 mol carboxylate groups.
The protonation step is analogous to the reversible protonation step illustrated

in Fig. 2.8 for an Al-OH^ 2 on the edge surface of kaolinite (seethe discussion
of acidic surface OH groups in sections 2.3 and 2.4). It creates a positively
charged water molecule at the mineral surface, an unstable surface species
with an instability that makes the ligand exchange (H2O for COO - ) in Eq.
3.12b more likely. Thus, ligand exchange is favored at pH values below which
the mineral surface bears a net positive charge (e.g., less than pH 5.4-up to 8.0
for allophanic minerals, as discussed in Section 2.3). The species =MOOC— S
on the right side of Eq. 3. 12b is similar in structure to the inner- sphere bridging
complex depicted in Figure 3.6, with the important difference that the metal M
involved is bound into the mineral structure. This fact and the trivalent charge
on the metal ion leads to a very strong complexbetween the humus carboxylate
moiety S — COO - and the mineral surface. If the humus moiety complexed
has hydrophobic domains now exposed to the soil solution, it is likely that
they will serve to bind to similar organic moieties in dissolved humus through
hydrophobic interactions (and, if polar units are included, through hydrogen
bonding), thus nucleating the construction of a supramolecular association
of humus components that is strongly anchored to the mineral surface. This
association evidently would grow in a disorganized layered fashion as dissolved
humus moieties continued to adsorb onto anchored humus moieties. Humus
nearest the mineral surface would thus be effectively protected from microbial
attack, whereas that exposed to the soil solution at the top of a multilayer patch
would be susceptible to desorption and to microbial attack.

For Further Reading

Chiou, C. T (2002) Partition and adsorption of organic contaminants in envi-
ronmental systems. Wiley-Interscience, Hoboken, NJ. Chapter 7 of this
useful monograph describes the theory and application of the Chiou dis-
tribution coefficient, including its estimation from statistical correlation
equations.

Clapp, C. E., M. H. B. Hayes, N. Senesi, P. R. Bloom, and P. M. Jardine
(eds.). (2001) Humic substances and chemical contaminants. Soil Sci-
ence Society of America, Madison WI. The 23 chapters of this edited
workshop/symposium offer a comprehensive survey of humic substance
structure, reactivity, and transport in soils.

Essington, M. E. (2004) Soil and water chemistry. CRC Press, Boca Raton,
FL. Chapter 4 of this textbook gives a comprehensive survey of humus
structure and reactivity, including an introduction to the spectroscopic
techniques used commonly to examine them. Chapter 7 provides an

86 The Chemistry of Soils

introduction to the concept and application of the Chiou distribution
coefficient.

The following five technical journal articles offer probing, advanced reviews of
the evolving concepts of humic substance structure and preservation in natural
soils.

Allison, S. D. (2006) Brown ground: A soil carbon analogue for the green world

hypothesis? Amer. Naturalist 167:619-627.
Baldock, J. A., and J. O. Skjemstad. (2000) Role of the soil matrix and minerals

in protecting natural organic materials against biological attack. Org.

Geochem. 31:697-710.
Burdon, J. (2001). Are the traditional concepts of the structures of humic

substances realistic? Soil Sci. 166:752-769.
Piccolo, A. (2001) The supramolecular structure of humic substances. Soil Sci.

166:810-832.
Sutton, R., and G. Sposito. (2005) Molecular structure in soil humic substances:

The new view. Environ. Sci. Technol. 39:9009-9015.

Problems

The more difficult problems are indicated by an asterisk.

1. Develop a reaction analogous to that for peptide formation in Eq. 3.1 to
demonstrate that cellulose is a condensation polymer of glucose.

*2. The Soil Science article by Piccolo (see "For Further Reading") offers
many lines of experimental evidence for humic acids to be pictured
as supramolecular associations of diverse components having relatively
small molecular size. On pages 820 to 821 of his article, Piccolo describes
the results of a study in which fractions of a humic acid treated with
acetic acid (Table 3.1) at pH 3.5 were compared regarding the types of C
they contained (e.g., aromatic C) with fractions of the humic acid not so
treated.

a. Give a chemical definition of supramolecular association. Be sure to
cite your source.

b. Piccolo states five findings concerning the composition of the
fractions of the humic acid treated with acetic acid that he concludes
are evidence for a supramolecular association. What are these five
pieces of evidence?

*3. The table presented here shows the mean content of nonmetal elements
in freshwater humic substances worldwide, taken from the same source
as the data in Table 3.3. Given the standard deviations for the mean
values, it is possible to compare them pairwise to determine whether
statistically significant differences exist between the compositions of soil

Soil Humus 87

and freshwater humic substances. This can be done with a two-sided
t test applied at a chosen level of significance — say, P < 0.01 (less than
one chance in 100 that the two compound mean values are equal, if t is
large enough).

a. Examine the two sets of composition data for significant differences
in C, H, and O content (P < 0.01). Take n = 215 for soil humic acids;
n = 56 for freshwater humic acids.

b. Compare the molar ratios O-to-C and H-to-C regarding whether
they are significantly different between soil and freshwater humic
acids (P < 0.01).

c. Is it accurate to state that soil humic acids are less polar and more
aromatic than freshwater humic acids?

(Hint: Use available software or online programs to perform the t tests.)

C(g kg" 1 ) H (g kg" 1 ) N(g kg" 1 ) S(g kg" 1 ) 0(g kg" 1 ) O/C H/C

512 ±30 47 ±16 26 ±6 19 ± 14 404 ± 38 0.60 ± 0.08 1.12 ± 0.17

4. Combine Eqs. 3.3 and 3.6 to derive a chemical equation for the cation
exchange of Ca 2+ for Na + on humus.

5. Apply the concept of cation exchange to explain why the pH of an acidic
suspension of humic acid with a 100 mol m background electrolyte
solution would be expected to be lower than that of a suspension with no
background electrolyte solution.

"6. The net proton charge for humic substances is described mathematically
by the two-term model equation

bi b 2

oh =

l + (Ki[H+])Pi 1 + (K 2 [H+])P2

where bi is the carboxyl content and b 2 is the phenolic OH content. The
parameter K; (i = 1, 2) represents the average affinity of either carboxyl
groups or phenolic OH groups for protons, whereas the parameter p; (i
= 1, 2) represents the variability within the two acidic functional groups
regarding affinity, with < p ; < 1, with the upper limit p; = 1.0 signify-
ing no variability. Examination of a large database for humic acids titrated
at low background electrolyte concentration produced the parameter
estimates

bi = 3.15 mol c kg" 1 , Ki = 10 2 ' 93 L mol" 1 , p x = 0.50
b 2 = 2.55 mol c kg" 1 , K 2 = 10 8 - 00 L mol" 1 , p 2 = 0.26

88 The Chemistry of Soils

The values of K;(i = 1,2) imply that half the carboxyl groups are disso-
ciated at pH 3, whereas half the phenolic OH groups dissociate at pH 8.
Both groups exhibit broad distributions of affinity for protons, because
P;(i = 1, 2) is not close to 1.0.

a. Prepare a graph of an versus -log[H + ] as in Figure 3.3.

b. Calculate ANC (in micromoles of charge per liter) in the pH range 4
to 7 for a suspension of humic acid having a solids concentration of
30 mg L _1 . (Assume that [H+] «s 10"P H .)

7. The total acidity (TA) of solid-phase humus is defined by the equation

CEC = TA - a H (o- H < 0)

Thus, TA is a quantitative measure of the capacity of humus to donate
protons under given conditions of temperature, pressure, and soil solu-
tion composition. Use the model equation and parameter values given in
Problem 6 to prepare a graph of the ratio TA-to-CEC versus — log[H + ]
over the pH range 3 to 9. (Take pH ~ — log[H + ].)

*8. Use the model equation and parameter values given in Problem 6 to
calculate the buffer intensity of the humic acid suspension in the range 4 to
7. {Hint: The first derivative with respect to x of 10~^ x is-(ln 10)P 10~ Px ,
where In 10 = 2.303. Use this result and the assumption that [H + ]
R« 10"P H with p H = dANC/dpH.)

*9. An adsorption edge is a graph of the moles of an adsorbed cation per
unit mass of solid phase versus pH (or — log[H + ]). Given that oh for
the humic acid with the titration behavior illustrated in Figure 3.3 can be
described by the model expression in Problem 6, plot the adsorption edge
for Na + (Eq. 3.6) using the following parameter values:

bi = 3.1mol c kg _1 ,Ki = 10 28 L mol" 1 ,p 1 = 0.48
b 2 = 2.7mol c kg" 1 , K 2 = 10 8 - 00 L mol" 1 , p 2 = 0.24

Take pH ~ — log[H + ] to lie in the range 4 to 9. The parameter pHso
is defined as the pH value at which the moles of adsorbed cation per
unit mass equal one half the maximal CEC. Estimate pHso from your
adsorption edge. (Hint: Show that the maximal CEC is equal to bi + b 2 .)

10. The table presented here lists water solubilities for two groups of organic
pollutant known to contaminate soils. Use these data to estimate the
Chiou distribution coefficient (L kg~ c ) for each pollutant. Look up the
chemical structures of the pollutants, then use this information to classify
them and explain the differences in log K oc among them.

Soil Humus 89

Pollutant

S(g m- 3 )

Pollutant

s(gm :

Chlorobenzene

484

Naphthalene

112

1,4-Dichlorobenzene

Phenanthrene

6.2

1,3,5-Trichlorobenzene

5.3

Anthracene

6.2

1,2,3, 5-Tetrachlorobenzene

3.6

Pyrene

0.90

Pentachlorobenzene

0.65

Benzanthracene

0.25

Hexachlorobenzene

5 x 10~ 3

Benzopyrene

4.9 x 10

11. The reported water solubility of the organic pollutant 1,2-
dichlorobenzene varies from 93 to 148 g m . Shown in the following
table are measured values of the Chiou distribution coefficient for this
pollutant on a variety of soils with varying organic C content. Estimate
log K oc for 1,2-dichlorobenzene based on its solubility, then compare your
result with the average of the measured log K oc , taking into account the
standard deviation for both your estimate and the average.

Soil

Koc (L kg" 1 )

Soil

Koc(Lkgo C 1 )

Anoka

261

Pierre

319

Burleigh

263

Piketon

263

Cathedral

407

Renslow

340

Columbus

308

Sanhedrin

344

Elliot

252

Spinks

318

Marlette

223

Wellsboro

383

Manchester

230

West- Central Iowa

248

Oliver

277

Woodburn

296

12. Ciprofloxacin ("Cipro") is a fluoroquinolone antibiotic that is becoming
widely distributed in soils through wastewater sludge disposal on land.
Concentrations of this antibiotic below 10 mg m -3 in the soil solution
are deemed acceptable, and some authorities have indicated a similar
threshold of 0.01 mg kg for its soil content. Given its water solubility
of 30 g L , what minimum soil organic C content is required to have
both the soil solution concentration and the soil content of Cipro at safe
levels? Are there soils for which this organic C content is typical?

13. Ceriodaphnia dubia is a freshwater invertebrate used for acute toxicity
tests involving pesticides and metals. When this organism is exposed to the
organophosphate pesticide chlorpyrifos at a concentration of 82 |xgm -3 ,
only 20% survival is found after 24 hours of exposure. If humic acid is
added, however, the percentage survival increases in a roughly propor-
tional manner, with 92% survival noted at a humic acid concentration of
100 gm -3 . The addition of humic acid at a concentration of 30 g m -3

90 The Chemistry of Soils

produced a survival rate of 50%, implying that the free concentration of
the pesticide was at its LC50 value. Given that log K oc = 3.79 for chlor-
pyrifos, and that the humic acid has a C content of 578 g kg -1 , calculate
LC50 for C. dubia exposure to the pesticide added at 82 |xgm -3 . Reported
values of LC50 range from 60 to 100 |xgm .

14. The desorption of PAHs from river sediments has been observed to follow
an exponential time dependence

n(t) = n exp(-k des t)

where no is an initial value of the amount adsorbed per unit mass of
sediments (see Eq. 3.10) and kd es is a rate coefficient for the desorption
process. Studies with a variety of PAHs, such as those listed in Problem
10, show that the value of ka es is correlated negatively with K oc for the
PAH compounds

logk d e S = -0.98 log K oc - 0.104

where k^ es is in units of day -1 . As shown in Eq. S.3.11 (in Special Topic
3 at the end of this chapter), the rate coefficient for an exponential time
dependence defines a half-life for the decline in n(t). Calculate this half-
life for each of the PAHs listed in Problem 10. This parameter defines an
intrinsic timescale for their desorption from the sediments.

*15. The table presented here shows measured values of recalcitrant humus
content and poorly crystalline Al and Fe oxyhydroxide content for the
fine clay fraction (< 0.2 |xm) in subsurface horizons in a dozen acidic
temperate-zone soils. Recalcitrant humus is defined as the humus remain-
ing in a soil sample after oxidation by NaOCl at pH 8. Poorly crystalline Al
and Fe oxyhydroxides are quantified by the content of Al and Fe extracted
by an ammonium oxalate/oxalic acid mixture at pH 3 . Apply linear regres-
sion analysis to these data to determine whether recalcitrant humus is
positively correlated with poorly crystalline Al and Fe oxyhydroxides, as
discussed in Section 3.5. Be sure to include 95% confidence intervals

Recal. humus Poor crys. oxides Recal. humus Poor crys. oxides

Soil (gkg- 1 ) (g kg- 1 ) Soil (g kg- 1 ) (gkg- 1 )

17.9

25.1

97.0

91.9

9.1

10.0

42.5

68.9

6.0

8.0

39.9

62.7

12.0

6.8

35.9

63.3

6.7

6.0

76.0

72.4

11.1

18.6

40.0

63.6

Abbreviations: Poor crys. oxides, poorly crystalline oxides; Recal. humus, recalcitrant
humus.

Soil Humus 91

on the y-intercept and slope of your regression line. Is there a thresh-
old content of poorly crystalline Al and Fe oxyhydroxides required for
the presence of recalcitrant humus? (Hint: Consider the 95% confidence
intervals in responding to this last question.)

Special Topic 3: Film Diffusion Kinetics in Cation Exchange

An adsorption reaction that involves chemical species in aqueous solution
must also involve a step in which these species move toward a reactive site on
a particle surface. For example, the Ca 2+ and H + species that appear in the
cation exchange reaction in Eq. 3.3 cannot react with the exposed surface site,
=SO~, until they exit the bulk aqueous solution phase to come into contact
with =SO~. Thus, the kinetics of surface reactions such as cation exchange
cannot be described solely in terms of surface site interactions unless the
transport step is very rapid when compared with the site interaction step. If,
on the contrary, the timescale for the transport step is either comparable with
or much longer than that for chemical reaction, the kinetics of adsorption will
reflect transport control, not reaction control. Rate laws must then be formulated
with parameters that represent physical, not chemical, processes.

This point can be appreciated more quantitatively after consideration
of an important (but simple) model of transport- controlled kinetics: the film
diffusion process. This process involves the movement of chemical species from
a bulk aqueous solution phase through a quiescent boundary layer (Nernst
film) to a particle surface. The thickness of this boundary layer, 8, will be larger
for particles that bind water strongly and smaller for aqueous solution phases
that are well stirred. The film diffusion mechanism in cation exchange is based
on two assumptions: (1) that a thin film of inhomogeneous solution separates
an exchanger particle surface from a homogeneous bulk solution and (2) that
the exchanging cations diffuse across the film much more rapidly than the
concentrations of these ions change in the bulk solution.

If we call] the rate at which a chemical species like Ca + arrives at a particle
surface, expressed per unit area of the latter (termed the flux to the particle
surface, in units of moles per square meter per second), and if diffusion is the
mechanism by which the species makes its way through the boundary layer,
the Fick rate law can be invoked to describe the process:

j = -rtHbulk ~ Hsurf) (S.3.1)

where [i]buik is the concentration of species i in the bulk aqueous solution
phase, [i] sur f is its concentration at the boundary layer-particle interface,
and D is its diffusion coefficient (units of square meters per second) in the
boundary layer. The Fick rate law is based on the premise that a difference in
adsorptive concentration across the boundary layer "drives" the adsorptive to
move through the layer. The transport parameter D is a quantitative measure

92 The Chemistry of Soils

of the effectiveness of the processes that respond to the concentration differ-
ence to bring the species to the particle surface. The rate of adsorption (units
of moles per cubic meter per second) based on Eq. S.3 . 1 is equal to the product
of the flux, the particle specific surface area, and the particle concentration in
the aqueous solution phase:

rate of adsorption (physical) = (Da s c s /8)([i]b u lk — Hsurf) (S.3. 2a)

where a s is the specific surface area of the particle and c s is its concentration
in the aqueous phase.

A simple rate law for the binding of the species i to a single reactive site on a
particle surface can be developed as the difference between a rate of adsorption,
proportional to the concentration of i at the boundary layer-particle interface
and to that of the reactive site, and a rate of desorption proportional to the
concentration of the bound species:

Rate of adsorption (chemical) = k ac j s [i] sur f[=SO _ ] — kd es [=SOi] (S.3. 2b)

where k ac j s and kfe are rate coefficients for the two opposing chemical pro-
cesses. If mass is to be conserved during the overall adsorption process, the
right sides of Eqs. S.3 .2a and S.3.2b must be equal:

(Da s c s /<5)([i] bu lk - Hsurf) = k a dsHsurf[=SO~] - k d es[=SOi] (S.3.3)

The film diffusion process thus supplies species i at a rate that is matched by
the subsequent chemical reaction through adjustment of the value of [i] sur f to
a steady-state value determined by the mass balance condition in Eq. S.3.3:

r ., k diff [i] bulk + k des [=SOi] ,c,a\

Hsurf = — : — j r „-_., (S.3.4)

kdiff + k ads [=SO ]

where

kdiff = E>a s c s /5 (S.3.5)

is a film diffusion rate coefficient. Equation S.3.4 can be substituted into either
of Eqs. S.3 .2a or S.3. 2b to calculate the overall rate of adsorption. If Eq. S.3 .2a
is selected, the final result is

rate of adsorption = kdiff

k a dsHbulk[=SO ] - k d es[=SOi]
kdiff + k a d s [=scr]

(S.3.6)

A comparison between the kinetics of film diffusion and chemical reaction
can be made by examining the denominator in Eq. S.3.6. Under the condition
kdiff 2> k a d s [=SO~], transport through the boundary layer is much more
rapid than the adsorption reaction, and Eq. S.3.6 takes the approximate form:

rate of adsorption ~ k a d s Hbulk [— SO _ ] — ^des [— SOi] (S.3. 7)

kdiff too

Soil Humus 93

which is like the rate law appearing in Eq. S.3.2b, but is expressed in terms
of the bulk concentration of the species i. In this limiting case, the kinetics
are fully reaction controlled. Under the opposite condition, kjjff <<C k ac j s [SR],
transport through the boundary layer is very slow compared with the chemical
reaction, and Eq. S.3.6 takes the approximate limiting form

rate of adsorption ~ kjjff ( [i]bulk f ^T I (S.3.8)

kdiff i°° \ k a a s [=so \J

The significance of the second term on the right side of Eq. S.3.8 is seen after
setting the left side of Eq. S.3.2b equal to zero and solving for [i] sur f :

i et l

kdes NSOi]

[i] rf=-^V r (S.3.9)

Usurf k ads [=SO"]

which gives the concentration of i produced at the particle surface when the
adsorption— desorption reaction has come to equilibrium (rate = 0). Thus Eq.
S.3.8 can be expressed in the more useful form

rate of adsorption ~ k diS ([i] bu]k - [i]^) (S.3.10)

kdiff 4-°°

In this limiting case, the chemical reaction produces a steady value of [i] su rf
and the kinetics are wholly transport controlled. Measurement of the rate of
adsorption accordingly would provide little or no chemical information about
the process.

The rate law in Eq. S.3.10 is of the mathematical form that leads to an
exponential time dependence of [i]bulk> with a time derivative that may be
equated to minus the rate at which the bulk concentration of species i decreases
as it engages in adsorption. The rate coefficient kjjff is related to the half-life
for the exponential decline in [i]bulk through the conventional expression

0.693 / 8 \ ,

ti /2 = - = 0.693 (S.3.11)

kdiff \Da s c s /

Typical ranges of value for the parameters on the right side of Eq. S.3.11 are
a s = 10 2 to 10 3 m 2 kg _1 ,D = 10" 9 m 2 s _1 , 8 = 10" 7 to 10" 5 m, and
c s = 10 to 10 kg m . These values lead to ty on the order of seconds to
hours.

The Soil Solution

4.1 Sampling the Soil Solution

The soil solution was introduced in Section 1.4 as a liquid water repository
for dissolved solids and gases. Speaking more precisely, one can define the
soil solution as the aqueous liquid phase in soil with a composition that is
influenced by exchanges of matter and energy with soil air, soil solid phases,
the biota, and the gravitational field of the earth (Fig. 1.2). This more precise
chemical concept identifies the soil solution as an open system (Section 1.1),
and its designation as a phase means two things: (1) that it has uniform
macroscopic properties (e.g., temperature and composition) and (2) that it
can be isolated from the soil profile and investigated experimentally in the
laboratory.

Uniformity of macroscopic properties obviously cannot be attributed to
the entire aqueous phase in a soil profile, but instead to a sufficiently small
element of volume in the profile (e.g., a soil ped or clod). Spatial variability in
the chemical properties of the soil solution at the pedon or landscape scale is
axiomatic, and temporal variability, even in a volume element the size of a ped,
is commonplace because of diurnal fluctuations and seasonal changes punc-
tuated by direct influence of the biota. On both larger and smaller timescales
than those typified by the variability of solar inputs, temporal variation in
the properties of the soil solution also occurs because of the kinetics of its
chemical reactions.

The problem of isolating a sample of the soil solution without artifacts
(a much more difficult task than isolation of a sample from the water column

The Soil Solution 95

in a river or lake) has not yet been solved, but several techniques for remov-
ing the aqueous phase from soil to the laboratory have been established as
operational compromises between chemical verisimilitude and analytical con-
venience. Among these techniques, the most widely applied in situ methods
are drainage water collection and vacuum extraction, whereas the common ex
situ methods include fluid displacement and extraction by vacuum, applied
pressure, or centrifugation. The in situ techniques are influenced by whatever
disturbance to a soil profile and, therefore, natural aggregate structure and
water flow patterns, has occurred because of their installation. More subtly,
they yield a sample of the soil solution that has a largely undefined "support
volume" (the multiply connected, three-dimensional soil unit with pore space
that provides the aqueous sample), and they differ in whether they provide
the flux composition or the resident composition of a soil solution. A flux com-
position, which is relevant to long-term chemical weathering (Section 1.5)
and, more broadly, to solute transport in soils, is measured in an aqueous
sample obtained by natural flow of the soil solution into a collector (e.g., a
pan lysimeter). A resident composition, which is relevant to nutrient uptake
by the biota in soil (Fig. 1.2), is obtained by removing an aqueous sample
instantaneously into a collector, an operation that can be only approximated
by vacuum extraction. If for no other reason than the difference in the regions
of pore space sampled (e.g., the macropores vs. the macropores plus meso-
pores), the flux composition will usually deviate significantly from the resident
composition of a soil solution. This deviation can become acute if a soil profile
receives periodic intense throughputs of water or exhibits a pronounced soil
structure with its attendant spectrum of timescales over which water carries
solutes around and within aggregates.

The ex situ methods perforce sample a disturbed soil, even if they use soil
cores, but they inherently permit more control with regard to the sampling of
the water- containing pore space. Fluid displacement utilizes either a miscible
solution replacing the indigenous soil solution as it flows down a column, or a
dense, unreactive immiscible liquid that replaces soil solution while beingforced
through a soil sample by centrifugation. High yield and low contamination
of the soil solution sample, which need not be water saturated, are possible
with this method. In the vacuum extraction method, the aqueous phase of a
soil (in situ, as discussed earlier, or a disturbed sample saturated previously
with water in the laboratory) is withdrawn through a filter by vacuum. This
method suffers from both negative and positive interferences caused by the filter
(principally from adsorption-desorption reactions with dissolved constituents)
when the extracted solution passes through it. There are also uncertainties
associated with the effect of vacuum extraction on the chemical reactions
between dissolved constituents and soil solid phases. If the soil sample has
been saturated with water prior to extraction, the composition of the extract
also may differ considerably from that of a soil solution at ambient water
content. Despite these difficulties — which are shared with the applied pressure
extraction and centrifugation methods — the vacuum extraction technique,

96 The Chemistry of Soils

once standardized, is convenient for routine analyses. It usually provides
aqueous solutions with a composition that reflects something of the reactions
between the soil solution and solid soil constituents that occur in nature.

For any of the common methods of obtaining soil solutions, however,
there is still the problem of the inherent porescale heterogeneity in soil aque-
ous phases caused by the electrical charge on soil particles, discussed in
sections 2.3, 2.4, and 3.3. This charge creates poorly defined zones of accu-
mulation or depletion of ions in the soil solution near soil particle surfaces,
with accumulation occurring for ions with a charge sign that is opposite
that of the neighboring surface, and exclusion for those with a charge sign
that is the same. Because of this phenomenon, successive increments of, say,
a vacuum-extracted soil solution that represent different regions near soil
particle surfaces will not have the same composition.

Standard laboratory procedures have been compiled in Methods of Soil
Analysis (see "For Further Reading" at the end of this chapter) for the deter-
mination of the chemical composition of extracted soil solutions. These data,
which provide total concentrations of dissolved (i.e., filterable under desig-
nated conditions) constituents, pH, conductivity, and so on, make up the
primary information needed for the quantitative description of soil solutions,
at known temperature and pressure, according to the principles of chemical
kinetics and thermodynamics.

4.2 Soluble Complexes

A complex is a unit comprising a central ion or molecule that is bound to one
or more other ions or molecules such that a stable molecular association is
maintained. Examples of soluble complexes formed in the soil solution are
given frequently throughout Chapters 1 to 3, mainly as proton complexes in
which anions are the central species and protons are the binding species (e.g.,
bicarbonate, HCO^~, mentioned in Section 1.4 as a principal chemical form
of C found in soil solutions). Other important soluble complexes mentioned
prominently are the mineral weathering products Si(OH)^j, silicic acid, and
AIC2O4, an oxalate complex of Al 3+ . In these latter complexes, OH - and
C20 4 ~ are the binding species, termed ligands, as noted in Section 1.5 in
conjunction with the definition of complexation as a key mineral weathering
reaction (Eq. 1.4). (Ligand is usually applied solely to binding species that are
anions or neutral molecules, but it is applicable as well to cationic binding
species like the protons in bicarbonate or H^PO^ - .) If two or more functional
groups in a single ligand are bound to a metal cation to form a complex,
it is termed a chelate. The AIC2O4 species is a chelate in which two COO -
groups in the oxalate ligand are bound to Al . The chelates of Fe + formed
by siderophores (Section 3.1) involve three functional groups in the ligand
and are especially stable. The propensity of a ligand to coordinate around a
metal cation using multiple donor atoms is called its denticity. Trihydroxamate

The Soil Solution 97

siderophores coordinate around a metal cation using both of the O atoms in
each of their — 0-N-C=0 functional groups. Because there are three hydrox-
amate groups in these ligands, they are hexadentate, which is optimal for the
octahedral coordination with O preferred by most metal cations of interest in
soils (Section 2.1). As a general rule, the higher its denticity, the more likely a
ligand is to form a very strong complex with a metal cation. Note that denticity
is strictly a property of ligands, not the complexes they form. Siderophores
are almost always hexadentate ligands, but their complexes with metal cations
are not termed hexadentate. The appropriate term for the complex is based
on the coordination number of its metal cation center, which is octahedral in
the case of most metal-siderophore complexes. Thus, for example, trihydrox-
amate siderophores are hexadentate ligands that form octahedral complexes
withFe 3+ .

If the central ion or molecule and the ligands forming a complex are in
direct contact, the complex is termed inner-sphere, whereas if one or more
water molecules is interposed between the central ion or molecule and the lig-
ands bound to it, the complex is outer-sphere. These two concepts were applied
in Section 3 .5 to bridging complexes between organic ligands and metal cations
adsorbed on a mineral surface (figs. 3.5 and 3.6), and to the complex formed
through ligand exchange (Eq. 3.12) between an organic ligand and a metal
cation bound into a mineral structure. Similarly, the soluble complex AIC2O4,
which predominates at low concentrations in acidic oxalate solutions, turns
out to be inner-sphere, as is the complex that forms between oxalate and Al(III)
bound into the structure of the Al oxide corundum (Section 2.1), the result
of a ligand exchange reaction. The octahedral complex between Al + and
water molecules, Al(H20) 6 , also is inner-sphere, but conventionally the term
solvation complex is applied to it instead. The free-ion species introduced in
Section 1.1 and represented throughout Chapters 1 through 3 by notation such
as Al 3+ or NO^~, are actually solvation complexes, reflecting the ubiquitous
interactions between charged species and water molecules (dipoles) in aqueous
solution (Section 1.2). Inner-sphere complexes usually are much more stable
than outer-sphere complexes because the latter cannot easily involve ionic or
covalent bonding (Section 2.1) between the central metal cation and ligand,
whereas the former can. Thus the "driving force" for inner-sphere complexes is
the energy gained through strong bond formation between the central metal
cation and ligand. For outer-sphere complexes, the energy gain from bond
formation is not so large and the driving force instead involves the disorder
induced in the coordination shell about the central metal cation by the binding
of the ligand, such as the disruption of the hydration shell that occurs when
an anion coordinates to a metal cation through its solvation complex to form
an electrostatic bond.

Table 4.1 lists the principal metal complexes found in well-aerated soil
solutions. The ordering of free-ion and complex species in each row from left
to right is roughly according to decreasing concentration typical for either
acidic or alkaline soils. A normal soil solution will easily contain 100 to 200

98 The Chemistry of Soils

different soluble complexes, many of them involving metal cations. The main
effect of pH on these complexes, evident in Table 4.1, is to favor free metal
cations and protonated anions at low pH, and carbonate or hydroxyl complexes
at high pH.

Metal complex formation is typically a very fast reaction (microsecond
to millisecond timescales) if humus ligands are not involved. Other com-
plexation reactions of importance in soil solutions, however, exhibit slower
reaction kinetics. A useful example is provided by the reaction of dissolved
CO2 with water to form the neutral proton complex H2CO3 (Problem 15 in
Chapter 1):

C0 2 + H 2 0(£)

H 2 CO°

(4.1)

where both CO2 and H2CO3 are dissolved species. (The species denoted CO2
is a free-molecule species, a solvation complex of C.) The net rate of forma-
tion of H2CO3 can be expressed mathematically by the time derivative of its
concentration, dfH^COjj/dt, where the square brackets represent a concen-
tration in moles per cubic decimeter (liter). It is common practice to assume
that the observed rate of a reaction like complex formation can be modeled

Table 4.1

Principal metal species in soil solutions.

Cation

Principal

species

Acidic soils

Alkaline soils

Na+

Mg 2 +

org a ,Al(OH)^ n

Al(OH)7

Si(OH)»

Si(OH)°

K+

Ca 2 +

Ca 2 +, CaHCO+, org a

CrOH 2 +

Cr(OH)7

HCrOT

CrO 2 -

Mn 2 +

Mn 2 +, MnHCO+

Fe 2+

FeCO°, Fe 2 +, FeHCO+

FeOH 2 +,

Fe(OH)^,

org a

Fe(OH)^, org 3

Ni 2 +

NiCO^, NiHCO+, Ni 2+

Na+

Mg 2 +

Al 3 +

Si 4 +

K+

Ca 2 +

Cr 3 +

Cr 6 +

Mn 2 +

Fe 2 +

Fe 3 +

Ni 2 +

Cu 2 +

Zn 2 +

Mo 6 +

Cd 2 +

Pb 2 +

org"

Zn 2 +

HMoOT

Cd 2 +,CdCr+

Pb 2 +,org a

CuCO°, org 3
ZnHCO+, org 3 , Zn z+
HMoOT, MoO 2-
Cd 2+ , CdCl+, CdHCOJ
PbCO^, PbHCO+, org

"Organic complexes.

The Soil Solution 99

mathematically by the difference of two terms:

d [H 2 CO°]

R f - R b (4.2)

where Rf and Rb each are functions of the composition of the solution in which
the reaction in Eq. 4.1 takes place, as well as being dependent on temperature
and pressure. It is to be emphasized that Eq. 4.2 need not have any direct
relationship to the mechanism by which H2CO3 actually forms. For example,
there may be intermediate chemical species that do not appear in the reaction
in Eq. 4.2, but nonetheless help to determine the observed rate and prevent it
from being modeled mechanistically by a simple difference expression. When-
ever Eq. 4.2 is appropriate, however, Rf and Rb are interpreted as the respective
rates of formation (forward reaction) and dissociation (backward reaction) of
H2CO3. It is common practice also to assume that these two rates are propor-
tional to powers of the concentrations of the reactants and products in the
reaction (Eq. 4.1):

L dt 3J = k f [C0 2 f [U 2 0f - k b [H 2 CO°] 6 (4.3a)

where kf, kb,a, |3, and 8 are parameters. The exponents a, fS, and 8 are each
termed the partial order of the reaction inEq. 4.1 with respect to the associated
species (e.g., ath order with respect to C0 2 ) . The sum (a + P) is the order of the
forward reaction, whereas 8 is the order of the backward reaction. The parameters
kf and kb are the rate coefficients of the formation (forward) and dissociation
(backward) reactions respectively. Each of the five parameters in Eq. 4.3a may
depend on solution composition, temperature, and pressure. Note that the
units of the two rate coefficients will depend on the values of the partial orders
of the reaction.

Equation 4.3a is termed a rate law, a mathematical model of the net rate
of a reaction containing parameters that must be determined experimentally.
Partial reaction orders can be measured directly by observing the dependence
of the rate on the concentration of a reactant or product in a series of experi-
ments designed to maintain that concentration at a predetermined value (e.g.,
reactant added in large excess relative to other species in the reaction). In the
particular case of Eq. 4.3a, the reactant H 2 0(£) is always at a much higher
concentration (55.4 mol dm ) than is C0 2 , and the rate law is convention-
ally simplified by combining the H 2 concentration with the forward rate
coefficient:

d[H 2 CO°l „ r „-„5

L dt 3J = kf= [C0 2 f - k b [H 2 CO°] a (4.3b)

where k^ = kf [H 2 0]^ is termed a pseudo rate coefficient. In this model form,
kb is a & -order backward rate coefficient and kf is a pseudo a-order forward rate
coefficient.

100 The Chemistry of Soils

Rate laws are often simplified further by assuming that a partial reaction
order is the same as the stoichiometric coefficient of the associated chemical
species in a reaction. In the current example, this assumption yields a = 8 = 1
[i.e., the (pseudo) forward and the backward rate coefficients are both first
order]:

d[H 2 CO°l
L dt 3J = k* [C0 2 ] - k b [H 2 CO°] (4.3c)

This formulation is useful because it permits a constraint to be imposed on
the two rate coefficients. At equilibrium, the left side of Eq. 4.3c is equal to
zero and the equation can be rearranged to yield

k? rH 2 co°i

^f = L_^ 3Je _ K (4 4)

k b [C0 2 ] e

where [ ] e is a concentration measured at equilibrium. The parameter defined
by the ratio of equilibrium concentrations is called a conditional equilibrium
constant for the reaction. It is "conditional" because it depends on solution
composition, temperature, and pressure, just as the two rate coefficients do. At
a given equilibrium solution composition, temperature, and pressure, K c can
be measured independently of kinetics and, therefore, applied to constrain the
values of the rate coefficients as indicated in Eq. 4.4.

Measured values of the two rate coefficients in Eq. 4.3c at 25 °C in pure
water range from 0.025 to 0.040 s _1 for kf and from 10 to 28 s _1 for k^. As
discussed in Special Topic 3 (Chapter 3), each of these two first-order rate
coefficients defines a half-life or intrinsic timescale for the process it represents
(either formation or dissociation of H 2 COj). The timescale for dissociation
follows from Eq. 4.3c after dropping the first term on the right side: ty (disso-
ciation) = 0.693/kj,. The timescale for the formation reaction follows similarly
after dropping the second term on the right side of Eq. 4.3c and rewriting the
left side as — d [C0 2 ]/dt, as implied by Eq. 4.1: ty (formation) = 0.693/kf .
Evidently the intrinsic timescale for the formation of H 2 CC>3 ranges from 17
to 27 s, whereas that for dissociation of the complex is much smaller, ranging
from 27 to 70 ms. These data indicate that the complex H^COj is labile relative
to the reactant species, hydrated C0 2 . According to Eq. 4.4, the conditional
stability constant for the formation of H^COj at 25 °C should range in value
from 1 to 4 x 10 -3 ; directly measured values range from 1.0 to 2.9 x 10 -3 .
It follows from the value of K c and Eq. 4.4 that about 99.7% of carbonic
acid, H 2 CO|, which comprises both hydrated C0 2 and the neutral complex
H^COj, is in fact hydrated C0 2 .

The concept of a half-life (or intrinsic timescale) can be extended to
reactions that are not first order. Table 4.2 summarizes graphical relationships
that produce straight lines for concentration measured as a decreasing function
of time during a chemical reaction that is far from equilibrium. The model

The Soil Solution 101

Table 4.2

Graphical analysis of Eq. 4.5.

Reaction order (b) Plotting variables

Slope

y-lntercept

Half-life 3

Zero [A] vs. time

One In [A] vs. time
Two 1/[A] vs. time

-K
-K

[A]o

ln[A]

1/[A]

[A] /2K
0.693/K
1/K[A]

a Valid only for positive- valued K, with [A]o equal to the initial concentration of species A.

rate law underlying the graphical relationships has the generic form

d [A] \ h

-^J=K[A] b (K>0) (4.5)

where A is a chemical species and b is the partial reaction order. Note that the
parameter K in Eq. 4.5 may be a pseudo b-order rate coefficient, the product
of a higher order rate coefficient with a concentration (maintained constant
during an experiment) raised to a power. The parameter b, like a, p\ or 8 in
Eq. 4.3a, need not be the same as the stoichiometric coefficient of species A
in the chemical reaction investigated, because rate laws are strictly empirical.
Table 4.2, then, lists the half-life of a reaction according to its order. This
parameter is equal to the time required for the concentration of species A to
decrease to one half its initial value.

4.3 Chemical Speciation

The total concentrations of dissolved constituents in a soil solution represent
the sum of "free" (i.e., solvation complex) and complexed forms of the con-
stituents that are stable enough to be considered well-defined chemical species.
The distribution of a given constituent among its possible chemical forms can
be described with conditional stability constants, like that in Eq. 4.4, if com-
plex formation and dissociation reactions are at equilibrium. This requirement
of stable states is often met on timescales of interest in natural soils: both
ion exchange (Section 3.3) and soluble-complex formation are usually fast
reactions. On the other hand, certain oxidation— reduction and precipitation-
dissolution reactions are so unfavorable kinetically that the reactants can be
assumed to be perfectly stable species on the timescale of a laboratory or afield
experiment. But these generalizations can fail in important special cases. The
half-lives for metal complex formation and dissociation reactions in aqueous
solution at concentrations typical for soils actually range over about 15 orders
of magnitude, from 10 s for the dissociation of outer-sphere complexes to
10 s for the formation of certain inner-sphere complexes. The two extremes
of this spectrum of timescales present no practical limitations on the applica-
bility of conditional stability constants to soil solutions, whereas the range of

102 The Chemistry of Soils

10 to 10 s (e.g., the formation of the inner-sphere complex AlF + ) requires
careful consideration of equilibration timescales.

The way in which conditional stability constants are used to calculate the
distribution of chemical species can be illustrated conveniently by considera-
tion of the forms of dissolved Al in an acidic soil solution. Suppose that the
pH of the soil solution is 4.0 and that the total concentration of Al is 10 mmol
m -3 . The concentrations of the complex- forming ligands sulfate and oxalate
have the values 50 and 10 mmol m -3 respectively. The significant complexes
between these ligands and Al are AlSO^ and ALOx + , where Ox refers to oxalate
(see Eq. 1.4 and Section 3.1). These complexes are not the only ones formed
with Al, SO4, or Ox, nor are the two ligands the only ones that form Al com-
plexes in the soil solution, but they will serve to introduce chemical speciation
calculations in a relatively simple manner.

According to the speciation concept, the total concentration of Al (Alt,
as determined, for example, by atomic emission spectrometry or by the
8-hydroxyquinoline method to exclude polymeric species) is the sum of free
and complexed forms:

A1 T = [Al 3+ ] + [AlOH 2+ ] + [A1SO+] + [AlOx+] (4.6)

where the square brackets denote species concentrations in moles per cubic
decimeter (liter). (The hydroxy species AlOH + is also an important one at
pH 4.) Each of the complex species in Eq. 4.6 can be described by a conditional
stability constant:

K2c
K3c

c=r I ^ 1 l-^mol-dm 3
[Al 3+ ] [OH"]

[A1SO+]

[AlOx+]
[Al 3+ ] [Ox 2 "]

^mol" 1 dm 3

(4.7a)

I'-'mor 1 dm 3

(4.7b)

i^mor 1 dm 3

(4.7c)

Common to each of the stability constant expressions is the concentration of
the free-ion species Al 3+ . Therefore, Eq. 4.6 can be factorized in the form

AlT = K+] j 1 + I^l + I^l + [^lj

I [ Al ] [ Al ] [ Al ] j

= [Al 3+ ] { 1 + Kic [OH - ] + K 2c [SO 2 "] + K 3c [Ox 2 "] } (4.8)

The ratio of [Al 3+ ] to Alt, termed the distribution coefficient for the species
Al 3+ , can be calculated with Eq. 4.8 if the concentrations of the free-ion species

The Soil Solution 103

of the four complexing ligands are known or can be estimated:
[Al 3+ ]

«A1

A1 T

l + Ki c [OH-] + K 2c [S02-] + K 3 c[0 X 2 -]} ' (4.9)

For OH , one can readily estimate the free-ion concentration using the
pH value:

[OH-I = ,% « ^j = 10P H " 14 mol dm" 3 (4.10)

L J [H+] 10"P h

where K wc is the ionization product of liquid water under the conditions
that exist in soil solution (hence the subscript c). For dilute solutions at
25 °C and under 1 atm pressure, K wc ss 10" 14 mol 2 dm" 6 and [H+] R« 10"P H
numerically. Thus, [OH - ] ~ 10 _10 mol dm - in the current example (pH 4).
For the other ligands in Eq. 4.9, the free-ion concentrations cannot be
calculated so directly. Given the large value of K3 C relative to K20 it is reasonable
to expect that [AlOx + ] will be nearly equal to Alx and Oxt in the current
example. Thus, in a first approximation, Eq. 4.7c can be used to estimate a^y:

[AlOx+] a A10x 1 6 . 3 !

— ^ — K3 C = 10 dm mol

[Al 3+ ] [Ox 2 "] otMOioxOxT a^Oxr

(4.11)

where

[AlOx+1 [Ox 2 "]

«A10x = — -, «Ox = — (4.12a)

Alt Oxt

are the distribution coefficients for AlOx + and Ox , respectively, and Oxt is
the total oxalate concentration. In Eq. 4.11, it has been assumed that a^iox ~ 1
and a^i ~ ao x > with the result that

a 2 M f* (K3COXT)" 1 = 10" 1

and aAi ~ 0.32. Thus, about 30% of Alt is in the form of Al . This approx-
imate result can be used to estimate the distribution coefficients for each
inorganic complex:

[AlOH 2+ ] [AlOH 2+ ]

«MOH = ^j = «m L 3+ J = a A1 Ki c [OH"] ^ 10" 2 (4.12b)

[A1SO+] [A1SO+] r , .,

«A1S04 = L ^ J = «M r Al 3+-| = a Al K 2c [SO 2 "] « 0.13 (4.12c)

where the free-ion sulfate concentration has been equated with the total sulfate
concentration in Eq. 4.12c.

104 The Chemistry of Soils

The assumption that a^iox ~ 1 is not consistent with the large value esti-
mated for aM. This estimate can be refined by considering the ligand speciation
in more detail:

S0 4T = [SO*"] + [A1SO+] = [SO^-] {l + K 2c [Al 3+ ]} (4.13a)

Ox T = [Ox 2- ] + [AlOx+] = [Ox - ] { 1 + K 3c [Al 3+ ] } (4.13b)

where use has been made again of Eqs. 4.7a through 4.7c. Given [Al + ]
= a^iAhf ~ 3.2 x 10 -6 mol dm - , the ligand distribution coefficients are
estimated as

«so 4

<»Ox

[so 2 4 -]

S0 4T

[Ox-]
Ox T

[l + K 2c [Al 3+ ]} ^1.0 (4.14a)

[l + K 3c [Al 3+ ]} _1 *0.67 (4.14b)

The revised value of a^yox that results from Eq. 4.14b is 0.67. Thus, about two
thirds of Alx is organically complexed and about one third either is complexed
with inorganic ligands or is in the free-ion form, which is typical for acidic soil
solutions containing dissolved organic ligands at concentrations comparable
with Alx-

This example, despite the approximate nature of the calculations, illus-
trates all of the salient features of a more exact chemical speciation calculation:
mass balance (Eq. 4.6), conditional stability constants (Eq. 4.7), distribution
coefficients (eqs. 4.12 and 4.14), and the iterative refinement of the distribu-
tion coefficients through additional mass balance on the ligands (eqs. 4.13
and 4.14). The approach illustrated can be applied to any soil solution for
which the significant aqueous species and their conditional stability constants
are known.

4.4 Predicting Chemical Speciation

The distribution of dissolved chemical species in a soil solution can be cal-
culated if three items of information are available: (1) the measured total
concentrations of the metals and ligands, along with a pH value; (2) the con-
ditional stability constants for all possible complexes of the metals and H + with
the ligands; and (3) expressions for the mass balance of each constituent in
terms of chemical species (i.e., free ions and complexes). A flowchart outlining
the method of calculation given these three items is shown in Figure 4.1.

Total concentration of the metals (Mt) and ligands (Lf), along with a pH
value, are the basic input data for the calculation. They are presumed known
for all important constituents of a soil solution. The speciation calculation
then proceeds on the assumption that mass balance expressions like eqs. 4.6
and 4.13 can be developed for each metal and ligand. The mass balance expres-
sions are converted into a set of coupled algebraic equations with the free-ion

The Soil Solution 105

( INPUT J

CONSTITUENT METALS AND LIGANDS
M T ,L T

MASS BALANCES
M T = [M m+ ] + 2v c [Mv c H-y Lv a (aq)]

L T = [L '" ] + 2v a [Mv c H 7 L Va (aq)]

ELIMINATION OF COMPLEXES
C Ks

NUMERICAL ALGORITHM ESTIMATE
FREE ION CONCENTRATIONS

f CONCENTRATION OF FREE IONIC SPECIES ^\
^ AND COMPLEXES J

<r"C0NVER

^"""^^ NO

GENCE?^^- 1

YES

f OUTPUT J

Figure 4.1. Flowchart outlining a chemical speciation calculation based on mass
balance and the use of conditional stability constants for complex formation (Eq. 4.16).

concentrations as unknowns by substitution for the complex concentrations,
as illustrated in Eq. 4.8. This step requires access to a database containing
the values of all relevant conditional stability constants. In general, for the
complex formation reaction

v c M m+ + yH+ + v a L 1_ = M VC H Y L

y-^va

(4.15)

the conditional stability constant is

K s ,

[M vc H y L va J
[M] vc [H]Y [L] va

(4.16)

106 The Chemistry of Soils

where v c ,y, and v a are stoichiometric coefficients. Equation 4.16 can always
be rearranged to express [M vc HyL va ] in terms of K sc and the three free-ion
concentrations. For example, the formation of the bicarbonate complex
CaHCOj can be expressed by the reaction

Ca+ + H+ + CO 2- = CaHCO+ (4.17a)

for which K sc ~ 10 1L5 dm mol~ at 25 °C in a dilute soil solution. Thus,
numerically,

... [CaHCO+1

10 = r ? +ir +ir 2 i ( 4J7b )

[Ca 2 +] [H+] [CO 2 "]

and the concentration of the complex follows as

[CaHCO+] = 10 1L5 [Ca 2+ ] [H+] [CO 2- ] (4.17c)

The algebraic equations with the free-ion concentrations as unknowns
can be solved numerically by standard algorithms based on estimated or
"guessed" values. The resulting free-ion concentrations then are used to calcu-
late the complex concentrations with expressions like Eq. 4.17c. The calculated
species concentrations are checked by introducing them into the mass bal-
ance equations to determine whether they sum numerically to the input total
concentrations. If they do within some acceptable error (say, 0.01% difference
from the input Mx or Lx), then the calculation is said to have converged and the
speciation results may be accepted. If convergence has not been achieved, then
the numerical calculation is repeated using the current speciation results to
generate new input estimates for the free-ion concentrations in the numerical
algorithm.

As a first example of a full chemical speciation calculation, one may return
to the example introduced in Section 4.3, an aqueous solution comprising Al,
SO4, and oxalate at pH 4. The results of a calculation using the program
MINEQL+ are shown in Table 4.3. (Note that percentage speciation is the same
as the set of distribution coefficients for a metal or ligand, after multiplication
of the coefficients by 100.) The numerical calculation involved consideration
of a total of 13 soluble complexes, including three proton complexes of the
two ligands. Table 4.3 indicates that the approximate calculation described
in Section 4.3 is qualitatively correct: The complex AlOx + and the free ions
Al 3+ ,S0 4 _ , and Ox 2- are the most important chemical species, as implied
by Eqs. 4.12 and 4.14. However, the complex AlSOJ" is at a lower concentra-
tion than the estimated value because of competition from a second oxalate
complex — Al(Ox)^" — not considered previously, which also has reduced the
concentration of AlOx + . The two oxalate complexes of Al + taken together
account for about two thirds of Alx and of Oxx, as concluded from the simpler
results of the estimation made in Section 4.3.

The Soil Solution 107

Table 4.3

Chemical speciation of an aqueous solution containing 10 mmol rrr 3 Al,
10 mmol m~ 3 oxalate, and 50 mmol rrr 3 sulfate at pH 4. a

Constituent Percentage speciation

Al A10x+ (50.5) , Al 3+ (29.5) , Al (Ox)~ (9.6) , A1SO+ (9.3)

Oxalate A10x+ (50.5) , Ox 2 " (22.0) , Al (Ox) J (19.1) , HOx~ (7.8)

Sulfate SO 2- ( 97 - 2 ) - A1SO+ (1.9)

a Speciation computed using MINEQL+ (www.mineql.com).

The species competition noted in connection with the interpretation of
Table 4.3 brings to mind the questions of whether other metal cations in a
soil solution would compete with Al 3+ for oxalate ligands and whether other
ligands than sulfate would compete with oxalate for Al 3+ . These questions
are addressed in Table 4.4, which shows the results of a speciation calcula-
tion performed using MINEQL+ and composition data for a Spodosol soil
solution at pH 4.3 sampled by the immiscible fluid displacement technique
(Section 4.1). Note that the total concentrations of the four additional metals
are much larger than that of Al, and that, except for nitrate, the same is true of
the total concentrations of the additional ligands when compared with oxalate.
Despite this large difference in concentrations, the percentage speciation of Al
and oxalate are rather similar in Table 4.4 to what appears in Table 4.3. The
reason for this similarity can be appreciated by considering Eq. 4.7c applied to
both Al 3+ and Ca 2+ , then noting that the ratio of the concentration of AlOx +
to that of CaOx is equal to the ratio of their respective conditional stability
constants times the ratio of their respective free-ion concentrations:

[AlOx+j K A1Q* [ A l 3 +]

[CaOx ] K^°* [Ca 2 +] K '

Even if the ratio of [Ca + ] to [Al + ] is very large (e.g., something like 10), the
ratio of [AlOx + ] to [CaOx ] willnotnecessarilybesmall unless the conditional
stability constants for the two complexes are comparable in value. In the
current example, the conditional stability constant for the formation of AlOx +
is 10 6 ' mol -1 dm 3 , whereas that for the formation of CaOx is 10 3 ' 2 mol -1
dm 3 . It follows that the Ca 2+ concentration would have to be about three
orders of magnitude larger than that of Al 3+ before the concentration of
CaOx would even begin to approximate that of AlOx + . The important point
here is that the concentrations of metal complexes in soils depend not only
on the concentration of the free metal ion (a capacity factor), but also on the
conditional stability constant (an intensity factor).

The methodological approach outlined in Figure 4.1 is widely used to
estimate the concentrations of metal and ligand species in extracted soil solu-
tions as a basis for understanding the mobility and bioavailability of nutrients

108 The Chemistry of Soils

Table 4.4

Composition and speciation of Spodosol soil solution (pH 4.3). a

Constituent Cj (mmol m~ 3 ) Percentage speciation

Ca 350 Ca 2 + (94.5), CaSO° (4.2), CaOx (1.1)

Mg 80 Mg 2 + (96.0) , MgSO° (3.4)

K 210 K+ (100)

Na 130 Na+ (100)

Al 25 A10x+ (42.4) , Al (Ox)~ (36.5) , A1SO+ (8.8) ,

Al 3+ (7.2), Al (Ox) 3- (4.6)
S0 4 310 SO 2- (93.1), CaSO° (4.7)

CI 820 Cl~ (100)

C 2 4 50 Al (Ox)~ (36.5) , Ox 2 " (23.1) , A10x+ (21.2) ,

CaOx (7.9) , Al (Oxff (6.9) , HOx~ (3.7)
N0 3 20 NO~ (100)

"Speciation computed using MINEQL+ (www.mineql.com).

or toxicants. There are, however, several important limitations on chemical
speciation calculations that should not be forgotten:

First, pertinent chemical reactions and, therefore, important chemical species,
may have been unintentionally omitted in formulating mass balance equations.
Conditional stability constants for the species included in the mass balance
equations may not be accurate, or in some other way may not be appropriate
for soil solutions. The compilation of stability constants by Smith and Martell
[Smith, R. M., and A. E. Martell. (2001) NIST standard reference database 46.
Critically selected stability constants of metal complexes database. U.S. Depart-
ment of Commerce, Gaithersburg, MD.] is perhaps the most useful source of
these parameters available. However, temperature and pressure variations may
require attention. Significant temperature gradients exist in nearly all natural
soils, but adequate data on the temperature dependence of conditional equi-
librium constants may not, because most available databases refer to 25 °C.
A major challenge also arises in respect to the suite of chemical species to be
considered when metal complexation by dissolved humus must be included
in a speciation calculation. Progress in meeting this difficult challenge has
been reviewed carefully by Dudal and Gerard [DudaLY., and F. Gerard. (2004)
Accounting for natural organic matter in aqueous chemical equilibrium mod-
els: A review of the theories and applications. Earth Sci. Rev. 66:199.]. Although
the biomolecules in humus, such as aliphatic organic acids and siderophores
(Section 3.1), play very important roles in the chemical speciation of metal
cations in soil solutions, dissolved and particulate humic substances often
dominate the suite of organic ligands that influence metal solubility and
bioavailability. The current picture of humic substances portrays them as
supramolecular associations of many diverse components held together by
hydrogen bonding and hydrophobic interactions (see Section 3 .2 and Problem
2 in Chapter 3). Despite this molecular-scale complexity, the principal acidic

The Soil Solution 109

functional groups in humic substances fall into just two classes — carboxyl and
phenolic OH groups — and these two classes are likely to be important con-
tributors to the metal- complexing properties of humic and fulvic acids. A key
issue to be addressed, therefore, in developing a model of metal speciation that
includes humic substances in the spirit of the approach taken in Section 4.2
is how to formulate metal cation interactions with carboxyl and phenolic OH
groups to express the concentration of the resulting metal-humic substance
complexes in terms of conditional stability constants and free-ion concen-
trations. When this key issue has been resolved, an appropriate mathematical
relationship then can be substituted into a mass balance equation that includes
the concentration of metal-humic substance complexes, just as Eq. 4.7c was
substituted into the mass balance equation for Al (Eq. 4.6) to express the
concentration of the Al— oxalate complex in terms of a conditional stability
constant and free-ion concentrations.

Second, analytical methods for the constituents in a soil solution may be
inadequate to distinguish among various physical and chemical forms (e.g.,
dissolved vs. particulate, oxidized vs. reduced, monomeric vs. polymeric). Labora-
tory methods that quantitate total elemental concentrations may inadvertently
include particulate forms because of inadequate extraction of a soil solution
(i.e., filterable forms of the element are included with truly dissolved forms).
Specialized techniques are usually required to distinguish between elements in
different oxidation states, as discussed in Methods of Soil Analysis. The prob-
lem of quantitating free-ion concentrations or the concentrations of specific
complexes, which is especially challenging, has been reviewed by Kalis et al.
[Kalis, E. J. J., W. Liping, F. Dousma, E. J. M. Temminghoff, and W. H. van
Riemsdijk. (2006) Measuring free metal ion concentrations in situ in natural
waters using the Donnan membrane technique. Environ. Sci. Technol. 40:955.]
The studies in which free-ion concentrations of metals have been measured
directly and compared with the results of chemical speciation calculations
are few in number, but generally report good agreement between the two
methodologies — say, within a factor of two over a broad concentration range
of relevance to soils.

Third, the kinetics of certain chemical reactions assumed to be at equilibrium
on the basis of studies of simpler aqueous solutions may be retarded in soil solutions
by the formation of intermediate species that do not exist in the simpler systems.
Oxidation-reduction reactions and mineral dissolution reactions can exhibit
inherently slow kinetics in the absence of catalysis or in the presence of ligands
that form exceptionally stable complexes. The situation becomes particularly
complicated when the timescale of interest overlaps that of the kinetics of
a reaction of interest, as can occur when the uptake of an element in the
soil solution by the biota is investigated. Under these conditions, chemical
speciation kinetics must be considered carefully, especially in regard to the
lability of metal— ligand complexes (i.e., the degree to which they do not persist
as stable molecular entities on timescales that are long compared with the
timescale of interest). Dynamic chemical speciation methodologies have been

110 The Chemistry of Soils

reviewed carefully by van Leeuwen et al. [van Leeuwen, H. P., R. M. Town,
J. Buffle, R. F. M. J. Cleven, W. Davison, J. Puy, W. H. van Riemsdijk, and
L. Sigg. (2005) Dynamic speciation analysis and bioavailability of metals in
aquatic systems. Environ. Sci. Technol. 39:8545.]

Fourth, and last, an equilibrium -based approach to chemical speciation
may be a poor approximation for a particular soil solution because of flows of
matter and energy in natural soils. The appropriate time-invariant state in a
soil solution may not be a state of equilibrium, but instead a steady state.
Alternatively, mass balance equations may be affected by flows of matter over
the timescales of interest in speciation calculation, transforming them from
static to dynamic quantities that require considerations of mass transport.
It is important in this respect to emphasize the essentially subjective — but
critical — initial decision regarding the "free-body cut" when applying a mass
balance approach (i.e., the choice of a closed model system that is to mimic
the actual open system in nature).

4.5 Thermodynamic Stability Constants

Conditional stability constants, as the name implies, vary with the composition
and total electrolyte concentration of the soil solution. For example, in a
very dilute solution, the conditional stability constant for the formation of
CaHCO^ (Eq. 4.17) has the value 3.4 x 10 11 drn'mol" 2 . In a solution of
50 mol m -3 NaCl it is 0.70 x 10 11 dm 6 mol" 2 , and in 50 mol m -3 CaCl 2
it is 0.37 x 10 11 dm mol -2 . This variability requires the compilation of a
different database each time a speciation calculation is performed, which is
not an efficient approach to the problem!

Instead, concepts in chemical thermodynamics maybe called on to define
a thermodynamic stability constant.This parameter is by definition independent
of chemical composition at a chosen temperature and pressure, usually 25 °C
(298.15 K) and 1 atm. For the complex formation reaction in Eq. 4.15, the
thermodynamic stability constant is defined by the equation

K s = (M vc H y L va )/(M) vc (H)^(L) ra (4.19)

where boldface parentheses refer to the thermodynamic activity of the chem-
ical species enclosed. Unlike K sc in Eq. 4.16, K s has a fixed value, regardless of
the composition of the soil solution. To make this assertion a reality, the activ-
ity of a species is related to its concentration (in moles per cubic decimeter)
through an activity coefficient:

(i) = y,[i] (4.20)

where i is some chemical species, like Ca + or MnSO°, and y; is its activity
coefficient. By convention, y; has the units cubic decimeters per mole such
that the activity has no units and the thermodynamic stability constant is
dimensionless.

The Soil Solution 111

Conventions and laboratory methods have been developed to measure y;,
(i), and K s in electrolyte solutions. All species activity coefficients, for example,
are required to approach the value 1.0 dm 3 mol -1 as a solution becomes
infinitely dilute. Thus, in the limit of infinite dilution, activities become equal
numerically to concentrations and K sc becomes equal numerically to K s . With
Eqs. 4.16, 4.19, and 4.20, one can derive the relationship

log K s = log K sc + log {ymhl/YmYhYl™

(4.21)

The second term on the right side of Eq. 4 .2 1 must vanish in the limit of infinite
dilution, so a graph of log K sc against a suitable concentration function must
extrapolate to log K s at zero concentration. Experiment and theory have shown
that a useful concentration function for this purpose is the ionic strength, I:

z M

(4.22)

where the sum is over all charged species (with valence Zk) in a solution.
The effective ionic strength is related closely to the conductivity of a solution.
Experimentation with soil solutions has indicated that the Marion-Babcock
equation,

logl = 1.159+ 1.009 log*

(4.23)

is accurate for ionic strengths up to about 0.3 mol dm . In Eq. 4.23, 1 is in units
of moles per cubic meter, and k, the conductivity, is in units of decisiemens
per meter (dS m _1 for a discussion of the units used, see the Appendix.)

Experimental and theoretical studies of electrolyte solutions have led to
semiempirical equations that relate species activity coefficients to the effective
ionic strength. For charged species (free ions or complexes), one uses the
Davies equation (at 25 °C):

los

-0.512 Zf

i + Vi

0.31

(4.24)

where Z; is the species valence. The accuracy of Eq. 4.24 can be tested after
substituting it into Eq. 4.21:

log K s = log K sc + 0.512

1 + VI

0.31

AZ Z

whe

AZ^

v c m 2 + y + v a £ 2

(v c m + y - v a iy

(4.25)

(4.26)

in terms of the valences of M, H, L, and M vc HyL w in Eq. 4.15. According
to the Davies equation, a graph of A log K = log K s - log K sc against the

112 The Chemistry of Soils

I = 0.1 mol dm- 3
t = 25 °C

AZ'

Figure 4.2. A test of Eq. 4.25 (line through the data points) at I = 0.1 mol dm~ 3
and25°C.

parameter AZ should be a straight line with a positive slope that varies with
the value of I, as indicated in Eq. 4.25. Figure 4.2 shows a verification of this
result at I = 0.1 mol dm -3 for 219 metal complexes for which A log K has
been measured and the corresponding AZ calculated. The line through the
data is Eq. 4.25, with I = 0.1 mol dm -3 .

For uncharged monovalent metal-ligand complexes, uncharged proton—
ligand complexes, and uncharged bivalent metal-ligand complexes, some
semiempirical equations for log y; are (25 °C)

-0.1921 , , , ,

log Yml = (M = Na + , K + , etc.

6 Y 0.0164 + 1 V '

log YHL = 0.11

log YML = -0.31 (M = Ca 2+ , Mg 2+ , etc.)

(4.27a)

(4.27b)
(4.27c)

fori < 0.1 mol dm -3 . These expressions conform to a theoretical requirement
for neutral species that log y becomes proportional to I in the infinite dilution
limit.

With equations for estimating y;, it is possible to calculate sets of con-
ditional stability constants under varying composition from a single set of
thermodynamic stability constants. For charged complexes, the necessary rela-
tionship is given in Eq. 4.25, whereas for uncharged complexes described with
Eq. 4.27, one of the three expressions for log y; must be added to the right side

The Soil Solution 113

of Eq. 4.25. For example, in the case of the bicarbonate complex CaHCOj , at
I = 0.05moldm~ 3 ,

V0.05

0.3 (0.05)

log K sc = 11.529-0.512

1 + V0.05
x 8 = 11.529 - 0.687 = 10.842

according to Eq. 4.25, after rearrangement to calculate log K sc . In the case of
H 2 CO^ at I = 0.05 mol dm -3 , Eq. 4.27b must be added to Eq. 4.25 and, with
K s = 7.36 x 10 13 ,

logK sc = 13.867 - 0.512[0.1677] x 4 + 0.1(0.05)
= 13.867 - 0.343 + 0.005 = 13.529

In a speciation calculation based on the flowchart in Figure 4.1, a database
of K s values would be used to create the required database of K sc values, as
illustrated earlier. An estimate of I (e.g., based on Eq. 4.23) would be needed
to do this, and the K sc database would be refined in each iteration along
with the species concentrations and the value of I in Eq. 4.22. Convergence
of the calculation then would result in a mutually consistent set of species
concentrations, K sc values, and calculated ionic strength.

The conceptual meaning of the activity of a chemical species stems from
the formal similarity between Eqs. 4.16 and 4.19. The conditional stability
constant is a convenient parameter with which to characterize equilibria, but
it is composition dependent, in that it does not correct for the electrostatic
interactions among species that must occur as their concentrations change.
In the limit of infinite dilution, these interactions die out, and the extrap-
olated value of K sc represents the chemical equilibrium of an ideal solution
wherein species interactions other than those involved to form a complex are
unimportant. Thus, the activities in Eq. 4.19 play the role of hypothetical con-
centrations of species in an ideal solution. But the real solution is not ideal
as its concentration increases, because species are brought closer together to
interact more strongly. When this occurs, K sc must begin to deviate from K s .
The activity coefficient then is introduced to correct the concentration factors
in K sc for nonideal species behavior and thereby restore the value of K s via
Eq. 4.21. This correction is expected to be larger for charged species than for
neutral complexes (dipoles), and larger as the species valence increases. These
trends are indeed apparent in the model expressions in eqs. 4.24 and 4.27.

For Further Reading

Langmuir, D. ( 1 997) Aqueous environmental geochemistry. Prentice Hall, Upper
Saddle River, NJ. Chapters 2 through 6 of this advanced textbook offer

114 The Chemistry of Soils

comprehensive discussions of aqueous chemical speciation, including two
chapters on carbonate chemistry.

Loeppert, R. H., A. P. Schwab, and S. Goldberg (eds.). (1995) Chemical
equilibrium and reaction models. Soil Science Society of America, Madi-
son, WI. A useful compendium of applications-oriented articles on
chemical speciation, including a discussion of how conditional stability
constants are screened for quality, by the creators of the National Insti-
tute of Standards and Technology (NIST) database (Section 4.4), and
descriptions of several computer programs for performing speciation
calculations.

Richens.D. T. (1997) The chemistry of aqua ions. Wiley, New York. Chapter 1 of
this advanced treatise surveys the experimental methods for characteriz-
ing aqueous species. Subsequent chapters provide details of the structure
and reactivity of aqueous species organized according to the groups of
the Periodic Table of elements.

Schecher, W. D., and D. C. McAvoy. (2001) MINEQL+: A chemical equilibrium
modeling system workbook. Environmental Research Software, Hallowell,
ME. A useful working guide to applying chemical speciation software,
based on one of the more popular computer programs.

Schwab, A. P. (2000) The soil solution, pp. B-85-B- 122. In: M. E. Sumner (ed.),
Handbook of soil science. CRC Press, Boca Raton, FL. This chapter surveys
the same material that appears in the current chapter, but in more detail
and with the explicit use of chemical thermodynamics.

Sparks, D. L. (Ed.). (1996) Methods of soil analysis: Part 3. Chemical methods.
Soil Science Society of America, Madison, WI. This is the standard ref-
erence work on laboratory methods for determining the concentrations
and speciation of chemical elements in soils and soil solutions.

Stumm, W., and J. J. Morgan. (1996) Aquatic chemistry. Wiley, New York.
Chapters 2 through 6 of this classic advanced textbook provide an excel-
lent reference for the technical details of aqueous chemical speciation,
including kinetics, with many applications to natural waters.

Problems

The more difficult problems are indicated by an asterisk.

1. In the table presented here are composition data for drainage waters
collected at the litter— soil interface and at a point 0.3 m below that interface
in a soil supporting a deciduous forest. Discuss possible causes for the
differences in pH, and in K and Ca concentrations between the two soil
solutions. Calculate the total moles of cation and anion charge per cubic
meter, as well as the net charge per cubic meter, for each soil solution.
Explain why the net charge in each case is not zero and why it is larger in
absolute value for the litter solution than for the subsoil solution.

The Soil Solution 115

Constituent (mmol m 3 )

Ca Mg Na K NH 4 N0 3 CI S0 4 pH

Litter

4.86

Soil

5.98

2. The temperature dependence of rate coefficients often can be expressed
mathematically by the Arrhenius equation:

log k = A - B/RT

where A and B are constant parameters, R is the molar gas constant (see
the Appendix), and T is absolute temperature. The value of B for the rate
coefficient kf in Eq. 4.7c is 59 kj mol , whereas that for the rate coefficient
k], is 63 kj mol -1 . Calculate the values of the two rate coefficients, their
associated intrinsic timescales, and the conditional stability constant for
the reaction in Eq. 4.1 at 15 °C.

3. Develop a rate law to describe the kinetics of the metal complexation
reaction

M 2+ + L e- = Ml 2-£

and apply it to the complexation of Cd + by the synthetic
chelating ligands EDTA 4_ (ethylenedinitrilotetraacetate), HEDTA 3-
[N-(2-hydroxyethyl)ethylenedinitrilotriacetate],and CDTA 4- (trans- 1,2-
cyclohexylenedinitrilo tetraacetate), for which the respective log K sc values
are 16.5, 13.7, and 19.7 in a 100 mol m electrolyte background
solution. Measured values of the rate coefficient for complex disso-
ciation are 1.8 x 10 -4 , 1.5 x 10 -3 , and 9.9 x 10 _6 s _1 respectively.
Calculate the second-order rate coefficient for the formation of each
complex. What are the intrinsic timescales associated with the two rate
coefficients if the initial concentration of Cd 2+ is 1 (tmol m -3 ? Plant
uptake of Cd + at this initial concentration occurs in timescales on
the order of several minutes. Does this fact imply a kinetic influence
on uptake could occur from either the formation or dissociation of the
Cd complexes?

4. Develop an appropriate rate law like that in Eq. 4.3a for the formation
of AlF 2+ from Al 3+ and F~. The value of kf for this reaction at 25 °C
is 110 dm 3 mol -1 s _1 at pH 3.9, and 726 dm 3 mol -1 s _1 at pH 4.9.
The Arrhenius parameter B = 25 kj mol - (see Problem 2). What are
the corresponding values of kf at 10 °C? Calculate the half-life for AlF +
formation at both pH and temperature values, given [Al 3+ ]o = [F~]o =
10 mmol m -3 .

116 The Chemistry of Soils

5. Dissolved CO2 can react directly with hydroxide ions to form bicarbonate:

C0 2 + OH" = HCO"

as an alternative to the reaction in Eq. 4.1. Develop a rate law for CO2 loss
by direct transformation to bicarbonate. Given kf = 8500 dm mol s
and kb = 2 x 10 s for this reaction at 25 °C, show that the pH value
above which the rate of loss of CO2 by reaction with OH - will exceed
that driven by the forward reaction in Eq. 4.1 is about 8.6.

*6. The film diffusion model discussed in Special Topic 3 (Chapter 3) can also
be applied to a gas diffusing across an air-water interface such as exists
in soil pores (Section 1.4). This interface is characterized by a boundary
layer that separates soil air from a bulk soil solution. An intrinsic timescale
for diffusion across this boundary layer can be defined by the ratio 8
to D, where the two parameters are the same as those that appear in
Eq. S.3.1 of Special Topic 3. The quantity [i] sur f in this latter equation is
now interpreted as a concentration at the soil air-soil solution interface.
Its value can be calculated using Henry's law (Eq. 1.1 and Table 1.6) if
the partial pressure of a gas in soil air is known. The quantity [i]bulk m
Eq. S.3.1 applies to the bulk soil solution and, therefore, is influenced
by chemical reactions in this phase. Take i = CO2 and consider the
loss of dissolved CO2 to form the neutral complex H2CO3 as a reaction
that could influence [CG>2]bulk (Eq. 4.1). Derive an equation for <5 cr j t ,
the boundary layer thickness above which diffusion of CO2 across the
boundary layer will be influenced by the kinetics of H2CO3 formation.
Given D = 2 x 10 -9 m 2 s _1 for CO2 in water, calculate the value of
<5 cr i t at 25 °C and interpret your result by comparison with typical soil
pore sizes. (Hint: Derive an equation for <5 cr ; t based on the timescales
for diffusion across the boundary layer and loss of CO2 to form H2CO3,
yielding <5 cr ; t ~ 0.2 mm.)

7. The mass balance of carbonate in a soil solution, ignoring complexes with
metals, can be expressed as

C0 3T = [H 2 CO*] + [HCO3-] + [CO 2- ]

Given the conditional stability constants (at 25 °C),

Ki c = [H2CO3*] / [H+] 2 [CO 2 "] ^ 10 16 - 7
K 2c = [HCO-] / [H+] [CO 2 "] % io 10 - 3

derive equations for the distribution coefficients of the three carbonate
species. Use the approximation [H + ] ~ 10 _p to estimate the range of
pH over which HCOj" is dominant. (Hint: See Problem 15 in Chapter 1
for the definition of H2CO|.)

The Soil Solution 117

8. Combine Ki c and K2 C in Problem 7 with Kh in Table 1.6 to derive the
equation

Kic/K 2c Kh = Pco 2 / [H + ] [HCO~] ss 10 7 - 8 atm dm 6 mol" 2

where Kh is the equilibrium constant for the formation of carbonic acid,
as in Eq. 2.11a. This equation shows that the CO2 partial pressure and
[HCOrlare sufficient to determine pH. Calculate the pH value in equi-
librium with [HC07] = 1 mmolm -3 and P C o 2 = 10~ 3 ' 5 or 10~ 2 atm
(the range typical for soils).

*9. The carbonate alkalinity of a soil solution is defined by the equation

Alk = [HCO~] + 2 [CO 2- ]

Use the conditional equilibrium constants in problems 7 and 8 to
calculate the carbonate alkalinity of the soil solutions described in
Problem 1, given Pco 2 = 10 atm. Carbonate alkalinity may be inter-
preted as the ANC (Section 3.3) of a soil solution that is contributed by
carbonate species. Estimate the ANC of each soil solution in Problem 1
that is contributed by dissolved humus. (Hint: Reconsider the charge bal-
ance calculations in Problem 1 in terms of carbonate alkalinity and humus
ANC.)

*10. The base 10 logarithm of the thermodynamic stability constant for the
formation of bicarbonate (HCOr) at 25 °C is 10.329 according to the
conventions used in Eq. 4.19 (v c = 0, y = 1, v a = 1; L = C0 3 J. Cal-
culate the value of pHd; s for H2CO3 and compare it with the values listed
in Table 3.1 and with the average value of 2.93 for the carboxyls in humic
acid (Problem 6 in Chapter 3). (Hint: Subtract log K2 for the forma-
tion of bicarbonate from that for the formation of H2CO3 and apply the
definition of pH^is-)

11. Given that AZ is usually positive, what general conclusion can be drawn
from Eq. 4.25 about the effect of increasing salinity on soluble complex
formation?

12. The value of log K s for the formation of AlSO^J" from Al 3+ and S0 4 ~, a
reaction expected when gypsum is added to an acidic soil (see Problem
12 in Chapter 2), is 3.89. Calculate log K sc in a soil solution that has
a conductivity of 2.4 dS m . Does increasing conductivity enhance or
diminish AlSOJ" formation?

*13. Show that the concentration of the complex CaHCO^ , in a soil solution
is proportional to the concentration of Ca + times the partial pressure of
CO2 in the soil atmosphere. Calculate the value of the constant of pro-
portionality and then compute values of the ratio [CaHCOj 1 / [Ca 2+ ]
over the typical range of Pco2 in soils.

118 The Chemistry of Soils

14. The conductivity of a soil solution saline enough to affect salt-sensitive
plants is 1.5 dS m . Calculate the activities of Ca + and CaSO^ in this
solution if the concentrations of Ca 2+ and S0 4 ~ are both 2.8 mol m -3 ,
and log K s for the formation of CaSO° is 2.36.

15. Calculate the effect of increasing the conductivity of a soil solution from
0.5 to 3.0 dS m _1 (low to high salinity) on the concentration of Si (OH)"
maintained at a constant activity of 10 -4 by solubility equilibrium with
quartz (SiC^).

Mineral Stability and Weathering

5.1 Dissolution Reactions

Soil minerals such as aluminosilicates and metal oxides have strong chemical
bonds between their cationic constituents and oxygen. Exchangeable ions on
the surfaces of these minerals (e.g., Na + and Mg + on a clay mineral or Cl _ on
a metal oxide) can be solvated by water molecules from the soil solution and
diffuse away quickly, but the framework ions cannot be dislodged so easily.
For their removal, it is necessary to create a strong perturbation of the bonds
holding them in the mineral structure, and this can be accomplished only by
a highly polarizing species, like the proton or a ligand that forms inner-sphere
complexes (Section 4.2).

Proton attack begins with H + adsorption by the anionic constituent of a
mineral (e.g., OH in a metal oxyhydroxide, CO3 in a carbonate, or PO4 in a
phosphate). This relatively rapid reaction is followed by the slower process of
polarizing the metal— anion bonds near the site of proton adsorption, with sub-
sequent detachment of the metal-anion complex. The two-step mechanism
involved is illustrated schematically for the edge surface of the mineral gibb-
site [y-Al(OH)3] in Figure 5.1. A similar process also is shown in Figure 5.1
for ligand attack. In this latter case, a strongly complexing ligand in the soil
solution (e.g., oxalate, F _ , or P0 4 ~) exchanges for a water molecule bound to
Al, as was illustrated in Eq. 3.12:

eAI - OH+(s) + F" = =AlF(s) + H 2 0(£) (5.1)

119

120 The Chemistry of Soils

Al (H 2 0)^

AIF (H z O)t

Figure 5.1. Two dissolution mechanisms for gibbsite. (1) Protonation of an edge
surface hydroxyl group to form OH^ and detachment of Al + as a solvation complex
(pH < 5). (2) Ligand exchange of OH^ for F~ and detachment of Al 3+ as the A1F 2+
complex.

with subsequent detachment of the AlF + complex, which then equilibrates
with F - in the soil solution, followed by adsorption of H + to form the species
= Al — OHJ once again. Detachment of the metal cation into the soil solution
is always the slowest step of a mineral dissolution process.

For soil minerals with ionic constituents that are readily solvated and
detached [e.g., NaCl (halite) or CaSC>4 • 2 H2O (gypsum)], or for exchange-
able ions adsorbed on insoluble minerals, the kinetics of dissolution can be
described in terms of the film diffusion mechanism introduced in Special
Topic 3. The dissolution reactions of these rather soluble minerals or exchange-
able ions are therefore transport controlled. For soil minerals like the clay
minerals, metal oxides, and most carbonates, however, the rate of disso-
lution is surface controlled and is observed to follow zero-order kinetics,
described mathematically in Table 4.2. If [A] is the aqueous-phase concen-
tration of an ionic constituent of a mineral (e.g., Al 3+ ), then the rate law for
surface-controlled dissolution is expressed by the equation

d[A]
dt

k d

(5.2)

where the parameter kj is a rate coefficient that is independent of [A], but
is a function of temperature, pressure, [H + ], and, if appropriate, the concen-
tration of a strongly complexing ligand promoting dissolution via the second
mechanism in Figure 5.1. Typically the pH dependence of kj has the roughly

-10

-11

Mineral Stability and Weathering 121

Kaolinite
25±2°C

9 •.

• o

7
PH

Figure 5.2. Dependence on pH of the logarithm of the mass-normalized rate of dis-
solution of kaolinite suspended in 1 mol m NaCl solution at 25 °C. Open circles are
data based on Al release; solid circles are based on Si release. Data from Huertas, F.J., L.
Chou, and R. Wollast (1999) Mechanism of kaolinite dissolution at room temperature
and pressure. Part II: Kinetic study. Geochim. Cosmochim. Acta 63: 3261-3275.

U-shape form illustrated in Figure 5.2 for kaolinite dissolution at 25 °C. The
dissolved species with a concentration that appears in the rate law (Eq. 5.2) is
Si(OH)^ in this example, but the rate of silica release has been mass normal-
ized (units of moles per kilogram per second) through division by the solids
concentration (kilograms per liter).

As introduced in Problem 7 of Chapter 2, when a zero-order rate law
applies, an intrinsic timescale can be associated with the kinetics of mineral
dissolution:

T^is = (M r x dissolution rate)

(5.3)

where M r is the relative molecular mass of the dissolving mineral and the
dissolution rate is in units of moles A per gram of mineral per second, as in
Figure 5.2. The value of x& s characterizes the timescale on which one mole of
a mineral will dissolve in water, thus allowing comparisons to be made among
minerals of differing composition and density. Figure 5.3 shows a graph of log
T dis plotted against the Si-to-O molar ratio for several of the primary silicates
listed in Table 2.3. The values of x^, which are expressed in years, pertain to
proton-promoted dissolution at pH 5 and 25 °C. Increasing Si-to-O, which
implies increasingly strong chemical bonds in a primary silicate (Section 1.3)
and, therefore, increasing resistance to weathering, is correlated positively with
the intrinsic timescale for dissolution. Note that the timescales for hornblende
and quartz, approximately one millennium and a few thousand millennia,
respectively, are consistent with the sharp drop in the content of hornblende
relative to quartz illustrated in Figure 2.6. The persistence of both minerals in

122 The Chemistry of Soils

6 -

5 -

2 -

0.2

—

Dissolution
Timescales

quartz i

for Primary
Silicates

^/muscovite

( hornblende

/_er

statite

^/ forsterite

I I

0.3

0.4

0.5

Si/O

Figure 5.3. Dependence on the Si-to-O molar ratio of the logarithm of the dissolution
timescale (Eq. 5.3) at pH 5 and 25 °C for primary silicates.

the chronosequence over timescales that appear to be much longer than T<ji s
is a reminder that rates of dissolution measured in the laboratory are typically
up to three orders of magnitude smaller than those measured in field studies.
This well-known discrepancy arises because of the great complexity of mineral
dissolution processes in natural soils, where temperature and water content,
organic and inorganic coatings on mineral surfaces, and near-equilibrium
solubility conditions intervene to obviate the simplicity of Eq. 5.2.

The rate expression in Eq. 5.2 applies to a surface-controlled mineral dis-
solution reaction after any ion exchange or solvation reactions have occurred,
but well before equilibrium between the mineral and the soil solution is
reached. The same consideration applies to transport-controlled dissolu-
tion reactions governed by an expression like Eq. S.3.10 in Special Topic 3
(Chapter 3). As equilibrium approaches, the rate of dissolution becomes influ-
enced by the stoichiometry of the dissolution reaction. Dissolution reactions
for the minerals albite, allophane, anorthite, biotite, calcite, chlorite, ortho-
clase, and smectite were illustrated in sections 1.5, 2.2, 2.3, and 2.5. (Some
of these reactions involved incongruent dissolution.) Two other important
examples are the dissolution reactions of gypsum and gibbsite:

CaSQ 4 • 2 H 2 0(s) = Ca 2+ + SO 2 " + 2 H 2 0(£)

Al(OH) 3 (s) = Al 3+ + 3 OH"

(5.4)
(5.5)

Following the chemical thermodynamics concepts introduced in Section 4.5,
one can define a dissolution equilibrium constant for the reactions in eqs. 5.4

Mineral Stability and Weathering 123

and 5.5:

Kdis = (Ca 2+ )(S02-)(H 2 0) 2 /(gypsum) (5.6)

Kdis = (Al 3+ )(OH-) 3 /(gibbsite) (5.7)

where the boldface parentheses indicate a thermodynamic activity of the
species they enclose. The solid-phase activities of gypsum and gibbsite are
defined to have unit value if the minerals exist in pure macrocrystalline form
at T = 298.15 K and 1 atm pressure. If, as often can be true in soils, the solid
phases are "contaminated" with minor elements (Section 1.3) or are not well
crystallized (Chapter 2), their activity will differ from 1.0.

The solubility product constant for gypsum or gibbsite is defined by the
equations

Kso = K dis (gypsum) (H 2 0) 2 = (Ca 2+ )(S0 2 ") (5.8)

K so = Kdis (gibbsite) = (Al 3+ )(OH") 3 (5.9)

By convention, K so = Kd; s numerically when the solid phase is pure and macro-
crystalline (no structural imperfections), and the aqueous solution phase is
infinitely dilute. In this case, the solid and water activities are both defined
as equal to 1.0. In the current example, K so = 2.5 x 10 -5 for gypsum, and
K so = 1.3 x 10 -34 for gibbsite, according to published compilations of ther-
modynamic data such as the NIST database mentioned in Section 4.4. Usually
K so values for hydroxide solids are reported as *K so , which is Kd; s for the
dissolution reaction that is obtained by replacing OH - with H + using the for-
mation reaction for liquid water. In the case of gibbsite, for example, one adds
3[OH~ + H+ = H 2 0(£)] toEq. 5.5 and replaces Eq. 5.9 with the definition

*K so = *Kdis (gibbsite) (H 2 0) 3 = (Al 3+ )/(H+) 3 (5.10)

Because the equilibrium constant for the water reaction is 10 , *K so = 10 x
1.3 x 10~ 34 = 1.3 x 10 8 . The right sides ofEqs. 5.8 through 5.10 contain the
ion activity product (IAP) corresponding to the solid phases that are dissolving.
For the dissolution reaction of a generic solid M a Lt,(s),

M a L b (s) = M m+ + \}~ (5.11)

the IAP is defined by the equation

IAP= (M m+ )(l/-) (5.12)

Evidently IAP = (Ca 2+ )(S0 2_ ) for gypsum and IAP = (Al 3+ )(OH") 3
[or (A1 3+ )(H + )" 3 ] for gibbsite.

According to the method discussed in Section 4.5, the IAP can be cal-
culated solely with data on the chemical speciation of a soil solution. Thus,
Eq. 5.12 can be evaluated regardless of whether the dissolution reaction in Eq. 5.11

124 The Chemistry of Soils

+ 2r

-1

-3

log K SO = -33.9±0.7

_i_

240

480

720

960

1200

Time (hr)

Gibbsite in an Oxisol

n = (Al 3+ ) (OhT) 3 /K S0

Figure 5.4. Time evolution of the relative saturation (Eq. 5.13) for gibbsite in an
Oxisol. Data from Marion, G.M., D.M. Hendricks, G.R. Dutt, and W.H. Fuller (1976)
Aluminum and silica solubility in soils. Soil Sci. 121: 76-85.

is actually at equilibrium. Used in this way, the IAP becomes a useful probe for
determining whether dissolution equilibrium actually has been achieved. This
kind of test is made by examining measured values of the relative saturation:

£2 = IAP/K S

(5.13)

If £2 < 1 within some tolerance interval determined by experimental preci-
sion, the soil solution is said to be under saturated; if £2 > 1, it is supersaturated;
and when a dissolution reaction is at equilibrium, £2=1, again within experi-
mental precision. Figure 5.4 shows the approach of £2 from undersaturation to
unit value in the soil solution of an Oxisol containing gibbsite (as confirmed by
X-ray diffraction analysis). Ion activity products [(Al + ) (OH - ) ] were deter-
mined in aliquots of leachate from the Oxisol during slow elution. After about
40 days of elution, £2 ~ 1.0, and thermodynamic equilibrium between the soil
solution and dissolving gibbsite may be assumed to have been achieved. Mat-
ters can become complicated, however, in the case of gibbsite precipitation,
both because of the formation of metastable Al-hydroxy polymers that trans-
form slowly in the aqueous solution phase and because of structural disorder
in the growing solid phase (Section 2.4). Under these obfuscating conditions,
the interpretation of measured values of £2 becomes problematic.

The quantitative role of £2 in dissolution-precipitation kinetics can be
sharpened by a rate-law analysis of the reaction in Eq. 5.11. As in Section 4.2,
the rate of increase of the concentration of M m+ can be postulated to be equal
to the difference of two functions, Ry and Rf,, which depend, respectively, on
powers of the concentrations of the reactant and products in Eq. 5.11. This
line of reasoning is analogous to that associated with Eqs. 4.2 and 4.3a. The

Mineral Stability and Weathering 125

overall rate law is then

drivr m "h

-^^ = k dis [M a L b f - k p [M m+ ni/-]^ (5.14a)

where kd; s and k p are rate coefficients; and a, f3, and 8 are partial reaction
orders. If the solid phase is in great excess during dissolution or precipitation,
its concentration factor can be absorbed into the dissolution rate coefficient
kj = kdi s [M a Lb] , as was done with H2O in Eq. 4.3b. If also it is assumed that
a = a, P = b, as done in connection with Eq. 4.3c, then the overall rate law

1 , J = k d - k p [M m+ ] a [L £ -] b (5.14b)

can be postulated, where kj and k p depend on temperature, pressure, soil
solution composition, and the nature of the dissolving solid phase. The rate
coefficients, by analogy with Eq. 4.4, are related to a conditional solubility
product constant:

K soc = [M m+ ] a [l/-] b = ka/kp (5.15)

The combination of Eqs. 5.13 to 5.15 now produces the model rate law

d[M m+ T

dt
where the relationship (cf. Eq. 4.21)

kd(l-£2) (5.16)

S2 C = [M m+ ] a [L € -] b /K SO c

= y^YL[M m+ ] a [L^] b /K S o

= (M m+ ) a (L € ") b /K so = Q. (5.17)

has been applied. Equation 5.16 demonstrates the role of Q. as a discriminant
in the kinetics of dissolution-precipitation reactions. If a soil solution is highly
undersaturated, £2 <JC 1, and Eq. 5.16 reduces to Eq. 5.2. Near equilibrium,
however, Q. ~ 1, and the rate of dissolution becomes very small, a complicating
characteristic of mineral weathering in natural soils.

5.2 Predicting Solubility Control: Activity-Ratio Diagrams

Graphical methods based on dissolution equilibria offer a simple and direct
approach to the interpretation of soil mineralogy data. The two most com-
mon methods are the activity-ratio diagram and the predominance diagram.
Although both methods ultimately tell the same story, each has features appeal-
ing to different aspects of the patterns of mineral stability in soils. They are
both designed to respond to the questions: Does a dissolving solid phase con-
trol the concentration of a given chemical element in a soil solution under

126 The Chemistry of Soils

given conditions? If so, which solid phase is it likely to be? This query, facile in
appearance, turns out to be complex in application, thus the abiding need for
qualitative analyses, despite the ever-increasing sophistication of quantitative
speciation calculations.

The construction of an activity-ratio diagram can be summarized in four
steps:

1. Identify a set of solid phases that contain a chemical element of interest
and are likely candidates for controlling its solubility. Write a reaction for
the congruent dissolution of each solid, with the free ionic species of the
element as one of the products. Be sure that the stoichiometric coefficient
of the free ion (metal or ligand) in each reaction is 1.0.

2. Compile values of K<j; s for the solid phases. Write an algebraic equation
for log Kai s in terms of log [activity] variables for the products and
reactants in the corresponding dissolution reaction. Rearrange the
equation to have log[(solid phase)/(free ion)] — the log activity ratio — on
the left side, with all other log [activity] variables on the right side.

3. Choose an independent log [activity] variable against which
log[(solid)/(free ion)] can be plotted for each solid phase. Select fixed
values for all other log[activity] variables, corresponding to an assumed
set of soil conditions.

4. Use the fixed activity values and that of log K^ to develop a linear relation
between log[(solid)/(free ion)] and the independent log [activity] variable
for each solid phase considered. Plot all of these equations on the same
graph.

For a chosen value of the log[activity] parameter that has been taken
as the independent variable, and under the assumption that all solid phases
have activity equal to 1.0, the solid phase that produces the largest value of
the logarithm of the activity ratio is the one that is most stable, because the
activity of the free ion is then smallest. This conclusion follows directly from
the fact that a solid phase, which produces the smallest soil solution activity
of a free ionic species, will also produce the smallest concentration of that
species. The tendency of an ion, if several solids containing it were to be
present initially, would be to diffuse to the region of the soil solution where its
concentration will be least [recall the discussion of Fick's law in Special Topic
3 (Chapter 3)]. Therefore, the less stable solid phases would continually be
dissolving to replenish the ions that diffuse away, leaving as the sole survivor
the solid phase capable of producing the smallest soil solution activity of the
ion (i.e., the most stable mineral that contains the ion).

As an example, consider an activity-ratio diagram for the control of
Al solubility by secondary minerals in an acidic soil. The Jackson-Sherman
weathering scenario (Table 1.7) tells us that, when soil profiles are leached free

Mineral Stability and Weathering 127

of silica with freshwater, 2:1 layer- type clay minerals are replaced by 1:1 layer-
type clay minerals, and ultimately these are replaced by metal oxyhydroxides.
This sequence of clay mineral transformations (discussed in Section 2.3) can
be represented by the successive congruent dissolution reactions of smectite,
kaolinite, and gibbsite at 25 °C:

M go.208[ Si 3.82Alo.l8]Ali.29Fe(III) .33 5 Mg 0445 Oio(OH) 2 (s)

+ 3.28H 2 0(£) + 6.72H+ = 1.47Al 3+ + 0.335Fe 3+

+ 0.653Mg 2+ + 3.82Si(OH)° logK dis = 3.2 (5.18a)

Si 2 Al 2 05(OH)4(s) + 6 H+ = 2A1 3+ + 2 Si(OH)^ + H 2 0(£)

logK dis = 7.43 (5.18b)

Al(OH) 3 (s) + 3H+ = A1 3+ + 3H 2 0(£) log* K dis = 8.11 (5.18c)

The solid-phase reactant in Eq. 5 . 1 8a is half a formula unit of montmorillonite,
with Mg 2+ as the interlayer exchangeable cation. Its dissolution reaction is a
generalization of that in Eq. 5.11 to the case of a multicomponent solid. The
value of K d ; s for the dissolution of kaolinite (also half a formula unit) reflects a
moderately well-crystallized solid phase. Poorly crystallized kaolinite — typical
of intensive soil weathering conditions — would yield log K so ~ 10.5. The
reaction for gibbsite dissolution differs from that in Eq. 5.7 by subtraction
of the water ionization reaction, with a corresponding change in the value of
log K d ; s (Eq. 5.10). Like kaolinite, gibbsite is assumed to be well crystallized;
poorly crystallized gibbsite would yield log *K so ~ 9.35.

Equation 5.18 can be used to construct an activity-ratio diagram for Al
solubility as influenced by the leaching of silicic acid [Si(OH) 4 ]. The equations
for log[(solid) (Al 3+ )] are as follows:

log[(montmorillonite)/(Al 3+ )] = -2.18 + 0.228 log(Fe 3+ )

+ 0.444 log(Mg 2+ ) + 4.57 pH + 2.6 log (Si(OH)°) - 2.23 log(H 2 0)

(5.19a)

log[(kaolinite)/(Al 3+ )] = -3.72 + 3 pH + log(Si(OH)^) + - log(H 2 0)

(5.19b)
log[(gibbsite)/(Al 3+ )] = -8.11 + 3 pH + 3 log(H 2 0) (5.19c)

Note that Eq. 5.18a and its log K d ; s value must be divided by 1.47, and that
Eq. 5.18b and its log K d ; s value must be divided by 2, before Eq. 5.19 can be
derived. If (Si(OH) 4 ) is to be the independent activity variable plotted, then
pH, (H 2 0), and the activities of Fe 3+ and Mg 2+ in the soil solution must
be prescribed. Useful working values are pH = 5, (H 2 0) = 1.0, (Fe 3+ ) =
10 -13 , and (Mg 2+ ) = 6 x 10 -3 . The resulting linear activity-ratio equations

128 The Chemistry of Soils

are then

log[(montmorillonite)/(Al 3+ )] = 16.72 + 2.6log(Si(OH)°) (5.20a)
log[(kaolinite)/(Al 3+ )] = 11.28 + log(Si(OH)!|) (5.20b)

log[(gibbsite)/(Al 3+ )] = 6.89 (5.20c)

The activity-ratio diagram resulting from plotting Eq. 5.20 is shown in
Figure 5.5. The portions of the three straight lines shown in bold depict
the largest values of the activity ratio as the activity of silicic acid decreases
from left to right in the graph. The range of silicic acid activity typical of
all but the most leached soils is indicated by two vertical lines denoting the
solubility of quartz [(Si(OH)°) = 10 -4 ] and poorly crystalline solid silica
[(Si(OH)!j) = 10 -2,7 ]. Thus, the effect of soil profile leaching is simulated by
moving from left to right along the x-axis. At (Si(OH)Jj) ~ 10 -2 ' 7 , which
reflects conditions during the intensive weathering of primary silicates in
an acidic soil, Figure 5.5 indicates that smectite is the most stable solid
phase with respect to solubility control on Al. As leaching and loss of sil-
ica proceed, the silicic acid activity will decrease, and when (Si(OH)^) falls
well below 10 -4 , gibbsite becomes the most stable Al-bearing solid phase.
This progression agrees with the Jackson-Sherman weathering sequence in
Table 1.7.

At a given silicic acid activity, the three lines in Figure 5.5 can be pic-
tured as a sequence of (Al 3+ ) "steps," in the sense that (Al 3+ ) decreases as
each line is crossed while moving upward in the diagram. If (Si(OH)°) is
controlled by poorly crystalline silica, for example, (Al 3+ ) becomes equal
successively to 10 -6,9 , 10 -8 ' 6 , and 10 -9,7 , as the lines representing gibbsite,
kaolinite, and smectite are crossed. This stepwise decrease in (Al 3+ ) not only
tracks the decreasing Al solubility of the minerals at pH 5, but also implies
a sequence of solid-phase precipitation that can occur in soils if intermedi-
ate solid phases form during the intensive weathering of primary silicates or
during Si biocycling via phytoliths (the name given to poorly crystalline silica
precipitated in plants, particularly grasses). This possibility is formalized in
the Gay-Lussac-Ostwald (GLO) Step Rule:

If the initial composition of a soil solution is such that several solid
phases can precipitate a given ion, the solid phase that forms first will
he the accessible one for which the activity ratio is nearest above its
initial value in the soil solution. Thereafter, the remaining accessible
solid phases will form in order of increasing activity ratio, with the rate
of formation of a solid phase in the sequence decreasing as its activity
ratio increases. In an open system, any one of the solid phases may be
maintained "indefinitely."

The GLO Step Rule is a qualitative empirical guide to the kinetics of pre-
cipitation from supersaturated solutions. In a closed system, a sequence of

Mineral Stability and Weathering 129

10, —

log(Si(OH)

Figure 5.5. Activity-ratio diagram for smectite (montmorillonite), kaolinite, and
gibbsite at pH 5 based on Eq. 5.20 with silicic acid activity as the independent variable.
A solubility "window" for Si02(s) is shown, ranging from that of amorphous silica to
that of quartz.

solid-phase intermediates is predicted that depends on the process by which
initial conditions of temperature, pressure, and composition result in the for-
mation of a series of increasingly stable states. Each of these states transforms
into the one of next greater stability more slowly than it itself came into being
(otherwise, intermediate solid phases would not be observed). The mechanis-
tic basis of this sequence of transformations maybe related to the fact that solid
phases exhibit a larger rate of precipitation from a supersaturated solution as
their solubility increases. In an open system, the input of matter can be such as
to maintain the initial composition fixed, with the result that the solid phase
will be preserved that has least stability consistent with that composition and
with the possible reaction pathways, despite its expected dissolution to form
more stable phases.

Applied to the activity-ratio diagram in Figure 5.5, the GLO Step Rule
implies that, for example, if (Al 3+ ) > 10" 7 at pH 5 and (Si(OH)^) = 10" 2 ' 7
in a closed system, the least stable phase, gibbsite, could precipitate before the
most stable phase, smectite, is formed. This possibility underlies Problem 9 in

130 The Chemistry of Soils

Chapter 2, which proposes kaolinite and gibbsite precipitation from feldspar
weathering instead of smectite precipitation (Eq. 2.6). Field observations con-
firm the existence of all three minerals represented in Figure 5.5 as weathering
products of feldspars. Poorly crystalline kaolinite or gibbsite, as mentioned
earlier, are associated with larger K so values that would decrease the constant
terms in Eqs. 3.19b and 3.19c to the values -5.25 and -10.8 respectively. Thus,
the horizontal line in Figure 5.5 would be plotted 1.24 log units lower, and the
kaolinite line would be shifted downward by 1 .53 log units. These changes cre-
ate "windows" of gibbsite and kaolinite stability between well-crystallized and
poorly crystallized forms that replace the single lines in the diagram and thus
enlarge the range of silicic acid activity over which smectite remains the most
stable solid phase, within the variability permitted by the windows. This kind
of variability and the typical (Si(OH)^) = 8 x 10 in acidic soils suggests that
smectite, kaolinite, and gibbsite will indeed coexist in active soil weathering
environments.

5.3 Coprecipitated Soil Minerals

Coprecipitated soil minerals (Section 1.3) provide ubiquitous evidence for
the diverse ionic composition of soil solutions. As discussed in Chapter 2,
specific examples of these mixed solid phases include the clay minerals, if
metals replace Si in the tetrahedral sheet or Al in the octahedral sheet; calcite,
if Mg, Sr, Fe, Mn, or Na replaces Ca; and hydroxy apatite [CasOF^PO^], if
Ca is replaced by Sr or other metals, or if OH is replaced by F or other ligands.
In coprecipitation through the formation of a solid solution, the resulting
solid phase is a homogeneous mass with its minor substituents distributed
uniformly. Thus the basic requirements for this type of coprecipitation are
the free diffusion and relatively high structural compatibility of the minor
substituents with the precipitate as it is forming. These conditions, incidentally,
often are met when minerals precipitate from a silicate melt to form the parent
materials of soils: Feldspars and micas are well-known examples of primary-
mineral solid solutions (Section 2.2).

The principal effect of coprecipitation is on the solubility of the elements
in the solid. If the soil solution is in equilibrium with a solid solution, the
activity in the aqueous phase of an ion that is a minor component of the solid
may be significantly smaller than what it would be in the presence of a pure
solid phase comprising the ion. This effect can be deduced from Eq. 5.11 after
noting that (M a Lb) <SC 1.0 could reflect a very small concentration of either
the metal M or the ligand L occurring as the compound M a Lt, in a mixed
solid phase. The value of K so would thus be much less than that of K<j; s , with
a corresponding reduction in the IAP. Often the dissolution of solid-solution
minerals in a soil will be dictated by complicated kinetic considerations, and
the prediction of the composition of the soil solution as influenced by these
solid phases will be quite difficult. However, if equilibrium exists between the

Mineral Stability and Weathering 131

solid and aqueous phases, or even if it is desired only to have a general under-
standing of reaction pathways, a thermodynamic description of a dissolving
solid-solution mineral can be valuable.

Suppose that a solid solution forms because of the coprecipitation of
two metal cations, M m+ and N n+ , with a ligand L . The components (end
members) of the solid solution are the compounds M a Lt and N c L d (s), where
am = lb and en = Id to ensure electroneutrality. For each component of the
solid, an expression analogous to Eqs. 5.8 and 5.9 can be developed:

(M m+ ) a (l/-) b = K M (M a L b ) (5.21a)

(N n +)C(L £- ) d = KN(NcId) (5.21b)

where Km and Kn are equilibrium constants for the dissolution of the two
pure solid phases. If it is assumed that the solid dissolves congruently while
retaining a constant composition, its dissolution reaction can be expressed
analogously to Eq. 5.11:

M a (i-x)N cc L b(1 _ x)+dx (s) = a(l - x)M m+ + cxN n+

+ [b(l - x) + dx\L l ~ (5.22)

where x is the stoichiometric coefficient of N c L d (taken to be the minor com-
ponent) in the solid. This reaction describes a dissolution equilibrium state
known as stoichiometric saturation. This state is possible if the timescales for
changes in the composition of the dissolving solid and for subsequent precip-
itation of any solid phase (i.e., incongruent dissolution) are much longer than
that for the congruent dissolution of the solid. Its existence must be estab-
lished experimentally. If Eq. 5.22 is applicable, a corresponding dissolution
equilibrium constant can be expressed as follows:

(y[m+\&(\-x) /-^n+\cx /-^£- \b(l-x)+dx

K| s = — (5.23)

(M a (i_ x )N cx Lb(i_ x ) + dA:)

and a solubility product constant K™ can be defined as the product of Kf
with the activity of the solid, analogous to Eq. 5.8 or Eq. 5.9. This approach
treats the solid as if it were a single phase with an activity equal to 1.0.

Solid solutions of diaspore (AlOOH) and goethite (FeOOH) are com-
monly observed in soils that are subject to flooding, with the value of x in the
mixed solid Fei_ x Al x OOH ranging up to 0.15 (see Problem 6 in Chapter 2).
Thus, diaspore is the minor component and the solid-solution mineral is
termed Al-goethite. By analogy with Eq. 5.9, the dissolution reactions of the
two solid-phase components can be expressed in the following form:

FeOOH(s) + 3H+ = Fe 3+ + 2H 2 0(£) log K dis = -0.36 (5.24a)

AlOOH (s) + 3 H+ = Al 3+ + 2 H 2 0(£) log K dis = 7.36 (5.24b)

132 The Chemistry of Soils

These two reactions do not quite fit the format of Eq. 5.21, but, as in the case
of gibbsite (Eq. 5.10), they can be adapted to it formally by setting (H2O) =
1.0and(l/-) b = (H+)- 3 :

(Fe 3+ )(H+)" 3 = 10"°- 36 (FeOOH) (5.25a)

(A1 3+ )(H+)" 3 = 10 736 (AlOOH) (5.25b)

Thus, (H + ) _1 plays the role of an aqueous "ligand" activity. Equation 5.22
thus takes the following form:

Fei_ x Al x O(OH)(s) + 3H+ = (1 - x)Fe 3+ + xAl 3+ + 2 H 2 0(£) (5.26)

with a solubility product constant like that in Eq. 5.10:

*K S S ^ = (Fe 3+ ) 1 - X (A1 3+ ) X (H+)- 3 (5.27)

The effect of Al-goethite on Al solubility can be illustrated through a recon-
sideration of the activity-ratio diagram in Figure 5.5, but with the system
simplified to comprise only kaolinite and gibbsite in addition to Al-goethite.
For (H2O) = 1.0, Eqs. 5.19b and 5.19c yield the activity ratios for kaolinite
and gibbsite:

log[(kaolinite)/(Al 3+ )] = -3.72 + 3 pH + log(Si(OH)°) (5.28a)

log[(gibbsite)/(Al 3+ )] = -8.11 + 3 pH (5.28b)

Equation 5.25b can be developed to have the same form and meaning as these
two expressions after dividing both sides by (AlOOH)*, where the asterisk
refers to pure single-phase diaspore, and then setting (AlOOH)/(AlOOH)*
equal to x, the stoichiometric coefficient of diaspore in Al-goethite:

log[(diaspore)*/(Al 3+ )] = -7.36 + 3pH - log x (5.28c)

The condition (AlOOH)/(AlOOH)* = x defines what is known as the ideal
solid solution model. It states that the change in diaspore activity by virtue of its
coprecipitation with goethite is modeled quantitatively simply through equat-
ing the activity of a solid in the solid solution to its stoichiometric coefficient
in the solid solution. (In general, the solid activity would be expected to be a
more complicated function of x.) The effect of this model is to increase the
activity ratio, because x < 1 and, therefore, log x < 0. Thus, solid solution
formation decreases Al solubility.

Inspection of Eq. 5.28 shows that the activity ratios for all three solids
have the same dependence on pH. Like gibbsite, the activity ratio for Al-
goethite will plot as a horizontal line. Because log x < 0, the activity ratio
satisfies the inequality —7.36 — logx > —8.11, and ideal Al-goethite exhibits
a larger activity ratio than gibbsite at any Al content. Thus, ideal Al-goethite
will be more stable than gibbsite, regardless of the activity of silicic acid or

Mineral Stability and Weathering 133

the pH value. The same conclusion holds for ideal Al-goethite relative to
kaolinite if logx — 3.64 — log(Si(OH);j), according to Eqs. 5.28a and c, with
(Si(OH)°) < 10 -3 ' 4 to avoid competition from smectite. At its maximum,
x = 0.33. Under this condition, (Si(OH)°) < 10~ 3 - 15 would be sufficient to
ensure Al-goethite stability against kaolinite. It follows that any x would result
in Al-goethite stability over kaolinite. These conclusions, of course, refer to
ideal Al-goethite and should be taken as illustrative. Careful studies of synthetic
Al-goethite indicate that it is not an ideal solid solution, but instead actually
exhibits some immiscibility of its two components.

5.4 Predicting Solubility Control: Predominance Diagrams

A predominance diagram is a two-dimensional field consisting of well-defined
regions with coordinate points that are specified by a pH value and the base 10
logarithm of a second relevant activity variable. The boundary lines that define
regions in the diagram are specified by equations based on thermodynamic
equilibrium constants. In each region of a predominance diagram, either a
particular solid phase containing an ion of interest or the free-ion species
itself in the aqueous solution contacting the solid will be predominant. Thus,
a predominance diagram gives information about changing relative stabilities,
at equilibrium, among the solid phases formed by an ion as the pH value and
one other activity variable are altered in a soil solution. The construction of
this representation of solubility equilibria is summarized as follows:

1. Establish a set of solid-phase species and obtain values of log K for all
independent reactions between the solid-phase species.

2. Unless other information is available, set the activities of liquid water
and all solid phases equal to 1.0. Set all gas-phase pressures at values
appropriate to soil conditions.

3. Develop each expression for log K into a relation between a log[activity]
variable and pH. In any relation involving aqueous species, choose
values for the activities of these species.

4. Plot all the expressions resulting from step 3 as boundary lines on the
same graph with pH as the x-axis variable.

These steps will be illustrated with the mineral dissolution reactions in
Eq. 5.18 so a comparison can be made between activity-ratio and predom-
inance diagrams. A corresponding set of chemical reactions that relates the
solid-phase species to one another is (again with half formula units for the
clay minerals):

Al 2 Si 2 5 (OH) 4 (s) + 5 H 2 0(£) = 2 Al(OH) 3 (s)

+ 2Si(OH)^ logK=-8.79 (5.29a)

134 The Chemistry of Soils

Mg . 20g [Si3.82Alo.i8]Ali. 29 Fe(III) .335M go . 445 Oio(OH) 2 (s) + 7.69 H 2 0(£)
+ 2.31 H+ = 1.47 Al(OH) 3 (s) + 3.82 Si(OH)!j + 0.653 Mg 2+

+ 0.335 Fe 3+ log*K = -8.72 (5.29b)

M go.208[ si 3.82Alo.i8]Ali. 29 Fe(III) .33 5 M g()445 Oio(OH) 2 (s) + 4.02 H 2 0(£)
+ 2.13H+ = 1.47Al 2 Si 2 5 (OH) 4 (s) + 2.35 Si(OH)^ + 0.653 Mg 2+

+ 0.335 Fe 3+ logK=-2.26 (5.29c)

These three chemical equations are algebraic combinations of Eq. 5.18
designed to relate the three minerals one pair at a time. They also represent
incongruent dissolution reactions (Sections 1.4 and 2.3 — note the resemblance
between the smectite dissolution reaction in Eq. 2.7a and that in Eq. 5.29c),
by contrast with the preparation of an activity— ratio diagram, which utilizes
congruent dissolution reactions.

Inspection of Eq. 5.29 suggests that the activities of H 2 0, Mg 2+ , Fe 3+ ,
and Si(OH) 4 are all candidates for the second aqueous-phase variable in a
predominance diagram. To preserve comparability with Figure 5.5, choose
(Si(OH) 4 ), with the other three activities fixed as before. These choices reduce
the general log K equations to the forms:

-8.79 = 2 log(Si(OH)^) - 5 log(H 2 0) (5.30a)

-8.72 = 3.82 log(Si(OH) 4 ) + 0.653 log(Mg 2+ ) + 0.335 log(Fe 3+ )

+ 2.3 lpH -7.69 log(H 2 0) (5.30b)

-2.26 = 2.35 log(Si(OH) 4 ) + 0.653 log(Mg 2+ ) + 0.335 log(Fe 3+ )

+ 2.3 lpH -4.02 log(H 2 0) (5.30c)

to the working boundary-line equations:

log(Si(OH) 4 ) = -4.40 (kaolinite-gibbsite) (5.31a)

log(Si(OH) 4 ) = -0.763 -0.605 pH (smectite-gibbsite) (5.31b)

log(Si(OH) 4 ) = 1.51 -0.983 pH (smectite-kaolinite) (5.31c)

Figure 5.6 shows these boundary lines for a range of pH values common
in acidic soils. At pH 5, the sequence of predominant solid phases predicted to
occur as the activity of silicic acid changes is in agreement with the sequence
predicted in Figure 5.5. Note that if quartz controls the activity of silicic acid
[log (Si(OH) 4 ) = —4], there is a shift from kaolinite to smectite predom-
inance at pH 5.6 (i.e., for pure water equilibrated with atmospheric C0 2 ).
If the kaolinite and gibbsite solubility windows described in Section 5.2 are
incorporated, it is necessary to reconsider Eq. 5.29 with log K = —8.2, —10.5,
and —4.5 respectively. The effect of these changes would be to enlarge the field

Mineral Stability and Weathering 135

s - 4

V Smectite

^V (Fe 3+ ) = 1CT 13

>^ (Mg 2+ ) = 6x 10" 3

Kaolinite ^v

Gibbsite

I I

4 5 6 7

Figure 5.6. Predominance diagram for the same set of secondary minerals and fixed
aqueous metal cation activities as in Figure 5.5.

of stability of smectite at the expense of both kaolinite and gibbsite. Thus,
poor crystallinity of these two latter minerals makes the persistence of less
stable smectite possible in soil profiles. If only gibbsite is assumed to be poorly
crystallized, then the stability fields of both kaolinite and smectite grow to
push that of gibbsite below a horizontal line at log (Si(OH)°) = —6.35.

5.5 Phosphate Transformations in Calcareous Soils

Alkaline soils in arid to subhumid environments typically contain significant
amounts of calcite (or magnesian calcite), the formation of which is mediated
biologically (Section 2.5). The proton-promoted dissolution reaction of calcite
is given in Eq. 2.9b:

CaC0 3 (s) + H+ = Ca 2+ + HCO;

(5.32)

for which log K<jj s = 1.849 at 25 °C, if the solid phase is well crystallized, and
logKdi s = 3.939 if it is very poorly crystallized. In an open system such as a soil
profile, CO2 plays a role in calcite formation that is quantified by combining
Eq. 5.32 with the pair of reactions (see Problem 6 in Chapter 4)

C0 2 (g) + H 2 0(£) = H 2 CO* logK H = -1.466 (5.33a)

H 2 CO* = H+ + HC07 logKi = -6.352 (5.33b)

136 The Chemistry of Soils

to derive the overall dissolution reaction:

CaC0 3 (s) + 2 H+ = Ca 2+ + H 2 0(£) + C0 2 (g) (5.34)

for which logK = 1.849 + 1.466 + 6.352 = 9.667 if the solid phase is well
crystallized, and log K = 11.757 otherwise. Equation 5.34 is convenient for
representing the solubility of calcite as controlled by pH and Pqo 2 following
the recipe given in Section 5.2:

log[(calcite)/(Ca 2+ )] = -logK + 2 pH + logP C o 2 + log(H 2 0)

= -logK + 2pH + log P C o 2 (5.35)

if (H 2 0) = 1 for convenience in applications. Equation 5.35 is suitable either
for inclusion in an activity-ratio diagram or for calculating the thermody-
namic activity of Ca 2+ in terms of pH and Pco 2 - It shows that solubility
control of Ca + by calcite is favored by high crystallinity (i.e., smaller log K),
pH, and C0 2 partial pressure. High crystallinity corresponds to a solid phase
more stable against dissolution, whereas high pH diminishes the availability of
H + to promote dissolution (Eq. 5.32), and high Pco 2 increases the abundance
of bicarbonate ions that promote precipitation (Eq. 5.33). Note that the calcite
solubility window ranges over about 2 log units, similar to the windows for
kaolinite and gibbsite (Section 5.2).

Suppose now that a "neutral-reaction" phosphate fertilizer containing
CaHPC>4-2H 2 (dicalcium phosphate dehydrate or brushite) is applied to
a calcareous soil. What solid phase is likely to control phosphate solubility
after equilibration? An answer to this question has been found in experi-
mental studies of the fate of phosphate fertilizers. Depending on soil water
content, there is a transformation of brushite to CaHPC>4 (dicalcium phos-
phate or monetite), followed by a slow transformation (weeks to months) to
CagH 2 (P04)6-5H 2 (octacalcium phosphate). Ultimately, Caio(OH) 2 (P04)6
(hydroxy apatite) is expected, although octacalcium phosphate may persist for
years if phosphate fertilizer is applied continually.

These phosphate transformations can be understood in terms of an
activity-ratio diagram involving the four Ca phosphates and calcite. The
relevant dissolution reactions for the phosphate solid phases are

CaHP0 4 -2H 2 0(s) = Ca+ + HPO 2- + 2 H 2 0(£) logK dis = -6.62

(5.36a)
CaHP0 4 (s) = Ca 2+ + HPO 2- logK dis = -6.90 (5.36b)

\ Ca 8 H 2 (P0 4 ) 6 • 5H 2 0(s) + \ H+(aq) = \ Ca 2+
6 3 3

+ HPO 2 " + -H 2 0(£) log K dis = -3.32 (5.36c)

Mineral Stability and Weathering 137

\ Caio(OH) 2 (P0 4 )6(s) + \ H+(aq) = \ Ca 2+ + HPO 2 "
6 5 5

+ - H 2 0(£) log K dis = -2.40 (5.36d)

In this soil fertility application, the free-ion activity of interest is (HP0 4 - ) and
Eq. 5.36 have been arranged so that the stoichiometric coefficient of HP0 4 -
is 1.0, following the steps outlined in Section 5.2. The activity of Ca 2+ in
Eq. 5.36 is controlled by calcite. Therefore, Eq. 5.34 with log K<j; s = 9.667 can
be multiplied by the stoichiometric coefficient of Ca 2+ and subtracted from
(i.e., reversed and added to) Eq. 5.36.

The HP0 4 - activity ratios can then be expressed in logarithmic form
showing only a dependence on pH and Pco 2 - For brushite (DCPDH), the
calculation runs as follows:

-6.62 = log(Ca 2+ ) + log(HP0 2 ") - log(DCPDH)

= 9.67 - 2pH - logP C o 2 - log[(DCPDH)/(HP0 2 -)]

and

log[(DCPDH)/(HP0 2 ")] = 16.29 - logP C o 2 - 2pH (5.37a)

Equation 5.35 with (CaCC>3) = (H2O) = 1.0 and log K = 9.667 were used to
obtain Eq. 5.37a. In a similar fashion, one can derive expressions for the three
other Ca phosphates:

log[(DCP)/(HP0 2 -)] = 16.57 - logP C o 2 - 2pH (5.37b)

log[(OCP)/(HP0 2 -)] = 16.21 - ^logP C o 2 -2pH (5.37c)

log[(HAP)/(HP0 2 ")] = 18.51 - ^logP c02 -2pH (5.37d)

where DCP refers to monetite and obvious abbreviations have been used for
the remaining two Ca phosphates. The range of log Pco 2 is from approxi-
mately -3.52 to -2.5 in coarse- textured calcareous soils, with the larger value
representing conditions of high biological activity that tends to occur in the
soil rhizosphere.

Figure 5.7 is an activity-ratio diagram for P solubility based on Eq. 5.37
and Pco 2 = 10 -3 ' 52 atm, which is the average value in the atmosphere. At any
pH value, the order of decreasing stability of the four Ca phosphates is clearly
hydroxyapatite (HAP) <JC octacalcium phosphate (OCP) > monetite (DCP) >
brushite (DCPDH), which means that hydroxyapatite should control P solu-
bility at equilibrium. The role of calcite as a mediator of P solubility can be
revealed by considering the effects of changing Pco 2 or calcite crystallinity on
the four parallel lines in Figure 5.7. For example, under rhizosphere condi-
tions, the partial pressure of CO2 is expected to be larger than its atmospheric

138 The Chemistry of Soils

value, and the crystallinity of the (biogenic) calcite formed is expected to be
less than that precipitated abiotically in a laboratory. Increasing Pco 2 at a fixed
pH will decrease (Ca 2+ ), according to Eq. 5.34, and accordingly will increase
P solubility, as implied by Eq. 5.37 (i.e., the parallel lines in Fig. 5.7 will shift
downward, with HAP and OCP shifting more than DCP or DCPDH because
of the higher Ca-to-P molar ratio of the former minerals). Decreasing calcite
crystallinity, on the other hand, will raise K& s for the reaction in Eq. 5.32,
which means that (Ca 2+ ) will increase, if pH and Pco 2 are constant, in turn
decreasing P solubility and shifting the lines in Figure 5.7 upward by varying
amounts. Thus, these two characteristics of biological activity act oppositely
on P solubility represented in Figure 5.7.

As discussed in Section 5.2 for the activity-ratio diagram in Figure 5.5,
the parallel lines in Figure 5.7 can be viewed as a sequence of HP0 4 - activity
"steps" in the sense that, at any fixed pH value, (HP0 4 _ ) decreases as each line
is traversed moving upward in the diagram. For example, at pH 7.5, (HP0 4 - )
equals successively 10 , 10 , 10 , and 10 as the lines are crossed
going from DCPDH to HAP. This monotonic lowering of (HP0 4 _ ) reflects
the decreasing solubility of each phosphate solid and mimics the observed
sequence of solid-phase transformations described earlier. Moreover, if the
initial pH value and HP0 4 _ activity in a calcareous soil solution define a

T3
"5

D> J —

Figure 5.7. Activity-ratio diagram for calcium phosphates in a calcareous soil under
atmospheric CO2 pressure. Abbreviations: DCP, monetite; DCPDH, brushite; HAP,
hydroxyapatite; OCP, octacalcium phosphate.

Mineral Stability and Weathering 139

point in the activity— ratio diagram situated between a pair of the lines in
the diagram, the solid phase expected to precipitate first is the one with the
solubility line closest above the initial point. For example, if (HP0 4 - ) ~ 3 x
10" 4 at pH 8, then OCP should precipitate, not DCPDH or DCP.

Applied to Figure 5.7, the GLO Step Rule (Section 5.2) indicates that,
if DCPDH is added to a calcareous soil, DCP (not HAP) will form first
by dissolution of DCPDH. Thereafter, DCP will dissolve and OCP will be
formed, with this process occurring more slowly than the DCPDH — > DCP
transformation. Finally, in a closed system, OCP will slowly dissolve in favor
of HAP formation. This overall sequence is what is observed experimen-
tally, and, in laboratory studies with Ca phosphate solutions maintained
supersaturated with respect to OCP, but undersaturated with respect to
DCPDH or DCP, OCP has been found to precipitate at a rate dependent on
Q, = (Ca 2+ ) 4/3 (HP04~)(H+)~ 2/3 /K dis , the appropriate relative saturation
variable (Eq. 5.16). In field soils, continual fertilizer applications could main-
tain supersaturation with respect to OCP and thus stabilize this Ca phosphate
for an indefinite period. The GLO Step Rule would predict this stability in an
open system. These ideas, however, must be tempered by the possibility that
soluble phosphate or calcium complexes, as well as plant uptake of phosphate,
could inhibit OCP formation, as could the precipitation of phosphate with
cations other than Ca .

For Further Reading

Dixon, J. B., and D. G. Schulze (eds.). (2002) Soil mineralogy with environmen-
tal applications. Soil Science Society of America, Madison, WI. Chapter 4
of this standard reference work gives a brief introduction to solubility
equilibria with applications to mineral weathering reactions.

Essington, M. E. (2004) Soil and water chemistry. CRC Press, Boca Raton, FL.
Chapter 6 of this advanced textbook may be consulted to learn more
about the applications of mineral solubility equilibria to contaminant
fate and chemical weathering.

Kinniburgh, D. G., and D. M. Cooper. (2004) Predominance and mineral sta-
bility diagrams revisited. Environ. Sci. Technol. 38:3641. This useful article
describes how to combine the approach in Section 5.4 with chemical
speciation calculations to obviate the need to fix any activity values.

Sumner, M. (ed.). (2000) Handbook of soil science. CRC Press, Boca Raton, FL.
Section F of this advanced treatise contains four chapters giving detailed
discussions of the weathering transformations of soil minerals informed
by concepts in dissolution equilibria and kinetics.

White, A. E, and S. L. Brantley (eds.). (1995) Chemical weathering rates of
silicate minerals. Vol. 3 1 . Reviews in mineralogy. Mineralogical Society of
America, Washington, DC. This advanced edited monograph offers com-
prehensive discussions of silicate mineral weathering from microscopic

140 The Chemistry of Soils

to field scales. Chapter 9, "Chemical Weathering Rates of Silicate Minerals
in Soils," is of particular relevance to the current chapter.

Problems

The more difficult problems are indicated by an asterisk.

1. The rate of dissolution of albite (NaAlSi 3 8 ) at 25 °C at pH < 6
can be described with Eq. 5.2, where A is Al and k<j = 10
(H + ) 1//2 molg -1 s _1 . Calculate the dissolution rates at pH 4.0 ("acid
rain") and 5.6. Compare the dissolution timescales of albite at the two
pH values. Given the Arrhenius parameter B = 60 kj mol -1 (Problem 2
in Chapter 4), compare the dissolution timescales at the two pH values
when the temperature is 12 °C.

2. The rate of dissolution of kaolinite [Si4Al40io(OH)g] as portrayed in
Figure 5.2 can be described by Eq. 5.2 with the empirical equation

k d = i - 8 - 28 (H + ) - 55 + 10" 10 - 45 + 10- 6 - 80 (OH-) - 75 (5.37)

over the pH range 1 to 13. Show that this rate law exhibits a minimum
as a function of pH, either by plotting a graph or by applying differential
calculus, and that the minimum value occurs at pH 6.8.

*3. Typically the distribution coefficient for Ca 2+ in the soil solutions of
arid-zone soils is about 0.75. Given this information and the data in
Problem 7 of Chapter 4, calculate the IAP for calcite in a soil solution
with pH 8, a conductivity of 2.5 dSm -1 , an HCO^~ concentration of
1 molm -3 , and a total Ca concentration of 3.8 molm -3 . (Answer: IAP =
y Ca 2+[Ca 2+ ]y C0 2-[C0 2 -] = 3.3 x 10" 9 )

*4. The rate of precipitation of calcite (CaCOs) near equilibrium follows
Eq. 5.16 (M m+ = Ca 2+ ) with k p = 0.75 ± 0.08 L mol" 1 s" 1 appearing
on the right side. Estimate the value of the dissolution rate coefficient kj.

5. Suppose that dissolved Pb enters an acid soil in runoff water. Lead
phosphates are often thought to be the solid phases controlling Pb solu-
bility in acid soils, the two most important minerals being tertiary lead
orthophosphate [Pb3(P04)2] and chloropyromorphite [Pb5(P04)3Cl].
The dissolution reactions for these two solid phases can be expressed by
the equations

Pb(P0 4 )2(s) + - H+ = Pb 2+ + - H 2 P07 logK dis = - 1.80

f\ ^ 1

Pb(P0 4 )3Ch(s) + - H+ = Pb 2+ + - H 2 P07 + - Cl"
logK dis =-5.01

Mineral Stability and Weathering 141

Prepare an activity-ratio diagram for Pb solubility control by these two
minerals. Use (H^PO^) = 10 and (Cl _ ) = 10 as fixed conditions.
Which solid phase is expected to control solubility? Does the conclusion
change if (Cl") = 10" 5 ?

6. The weathering of the feldspar anorthite (CaAl2Si20s) to form calcite
and montmorillonite in soils (Eq. 2.8) is thought to be limited by unfa-
vorable kinetics of calcite precipitation, which causes the activity of Ca 2+
to remain larger than what K so for calcite would predict at a given activity
of C0 3 ~. This hypothesis implies that the activity of Ca + in equilibrium
with anorthite is larger than that in the presence of calcite. Check this
assertion by preparing an activity-ratio diagram for Ca solubility control
by the two minerals. The congruent dissolution reaction for anorthite is

CaAl 2 Si 2 8 (s) + 8H+ = Ca 2+ + 2Al 3+ + 2Si(OH)^
logK dis = 24.6

Assume that Eqs. 5.19c and 5.35 apply, and that the activity of silicic acid
is controlled by quartz.

7. The dissolution reaction in Eq. 5 . 1 8c has different log * K<jj s values depend-
ing on the crystallinity of the dissolving gibbsite phase. Prepare an
activity-ratio diagram for Al solubility control by gibbsite of differing
crystallinity and apply the GLO Step Rule to explain why poorly crys-
talline gibbsite is likely to be the first solid phase precipitated at pH 5
from soil solutions in which the Al 3+ concentration exceeds 2 mmol m -3 .
Estimate the Al 3+ activity in the soil solution with the chemical specia-
tion described in Table 4.4 and plot it on your activity-ratio diagram.
Is gibbsite precipitation expected at this (Al + )? Would your response to
this question be different if oxalate were not present? Explain.

8. The transformation of anorthite to montmorillonite and calcite (Eq. 2.8
and Problem 6) is favored by Si(OH)^ activities near 10 and pH values
near 8.5. In calcareous soils, however, it is often observed that gibbsite
forms instead of smectite when anorthite dissolves incongruently. Use
Eqs. 5.19a through 5.19c to construct an activity-ratio diagram at pH
8 like Figure 5.5, then invoke the GLO Step Rule to explain how, when
anorthite dissolves, gibbsite may form before montmorillonite.

9. According to the Jackson-Sherman weathering stages (Table 1.7), kaolin-
ite and gibbsite formation are favored by intensive leaching of a soil profile
with freshwater. This trend also implies that these two minerals will be
disfavored by low levels of soil moisture or by saline waters, both of which
are associated with a water activity less than 1.0. Examine this possibility
by constructing an activity-ratio diagram like that in Figure 5.5, but with
(H2O) = 0.5 instead of 1.0. Take pH and all other log[activity] variables
to have the same values as were used in constructing Figure 5.5. Compare

142 The Chemistry of Soils

your results with this latter figure. Is smectite favored over a broader range
of (Si(OH)°) as the water activity decreases?

10. Examine the effect of solid-phase crystallinity on the activity-ratio dia-
gram in Figure 5.5. Prepare activity— ratio diagrams using the alternative
values of log K^is for poorly crystalline kaolinite and gibbsite. What
is the overall trend in mineral stability among an assembly compris-
ing montmorillonite-kaolinite-gibbsite as crystallinity decreases and the
silica concentration diminishes at pH 5?

11. Prepare an activity-ratio diagram for the two lead phosphates described
in Problem 5 using log (HP0 4 - ) as the x-axis variable. Select pH 8 and
(Cl~) = 10~ 3 , noting that

H 2 PO~ = HPO 2- + H+ logK = -7.198

Plot lines corresponding to the Ca phosphate dissolution reactions
in Eq. 5.36, assuming that calcite controls Ca solubility and Pco 2 =
10 -3 ' 52 atm. Given your results, which Ca phosphate is best to add to
a calcareous soil to immobilize Pb as an insoluble phosphate solid?

1 2 . As indicated in Section 1 .3 ( Table 1.5), Cd may coprecipitate with calcite to
form a solid solution of CdC03 (otavite) and CaC03. When this happens,
the activity of CdCG>3(s) is not 1.0, but instead is equal approximately to
the fractional stoichiometric coefficient of Cd (ideal solid solution). Given
that log Kdj s = —12.1 for CdCC^s), calculate the corresponding log K so
for a coprecipitate of otavite and calcite containing 6.3 mol% CdC03.
Show that the activity of Cd 2+ produced in the soil solution by this mixed
solid is 1/16 that which would be produced by pure otavite under the
same conditions of temperature, pressure, and soil solution composition.

*13. The clay mineralogy of a forested soil chronosequence developed on vol-
canic ash parent materials exhibits a transformation from proto-imogolite
allophane (Si 2 Ai40io • 5 H2O) dominance to kaolinite dominance over
a period of several thousand millennia. During this time, the silicic acid
concentration and pH of the soil solution both decrease, from respec-
tive initial values of 0.3molm and 7.0 to respective final values of
5.6 mmolm -3 and 4.6. Given the congruent dissolution reaction

Si 2 Al 4 Oio -5H 2 0(s) + 12 H+ = 4 Al 3+ + 2 Si(OH)° + 7H 2 0(£)
logK dis = 26.0

prepare an activity-ratio diagram with log (Si(OH)!j) as the indepen-
dent variable to examine solid-phase controls on Al solubility. Use your
diagram to discuss the mineralogical transformations observed in the
soil chronosequence. (Hint: Be sure to consider the effect of kaolinite
crystallinity on your calculations.)

Mineral Stability and Weathering 143

14. Prepare a predominance diagram for proto-imogolite allophane and
kaolinite based on the dissolution reaction in Problem 13. Use exactly
the same coordinate axes as those that appear in Figure 5.7. Plot the soil
solution data given in Problem 13 on your diagram and discuss the min-
eralogical transformations observed in the soil chronosequence. A sharp
decline in allophane content and a corresponding increase in kaolinite
content is noted in the chronosequence when pH = 5.2 and (Si(OH)°) =
10" 4 - 6 .

15. Prepare activity-ratio diagrams analogous to that in Figure 5.7 to verify
the conclusions drawn in Section 5.5 concerning the effects of calcite
crystallinity and CO2 partial pressure. At what rhizosphere Pco 2 W1 U there
be no effect of decreasing calcite crystallinity on P solubility as predicted
by the activity-ratio diagram?

Oxidation-Reduction Reactions

6.1 Flooded Soils

Almost all soils become flooded occasionally by rainwater or runoff, and
a significant portion of soils globally underlies highly productive wetlands
ecosystems that are intermittently or permanently inundated by water bod-
ies. Peat-producing wetlands (bogs and fens) account for about half of these
inundated soils, with swamps and rice fields each accounting for about one
sixth more. Wetlands soils hold about one third of the total nonfossil fuel
organic C that is stored below the land surface (i.e., about the same amount
of C as is found in the atmosphere or in the terrestrial biosphere). This statis-
tic is all the more impressive upon learning that wetlands cover only about
8% of the global land area. On the other hand, they are significant locales
for denitrification processes, and they constitute the largest single source of
methane entering the atmosphere, emitting half the global total and, therefore,
contributing palpably to the stock of greenhouse gases (Section 1.1).

A soil inundated by water is essentially precluded from exchanging gases
with the atmosphere, resulting in the depletion of oxygen and the subsequent
accumulation of CO2 because of metabolic processes engaged in by the biota.
If sufficient labile humus (i.e., humus readily metabolized by microbes) is
available to support respiration (problems 2 and 3 in Chapter 1), then a char-
acteristic sequence of chemical reactions is observed in any submerged soil
environment. This sequence is illustrated in Figure 6.1 for two agricultural
soils: a German Inceptisol under cereal cultivation and a Philippines Vertisol
under paddy rice cultivation. In the former soil, which was maintained in a

144

Oxidation-Reduction Reactions 145

well- aerated condition prior to inundation, nitrate is observed to disappear
first from the soil solution, after which Mn(II) and Fe(II) begin to appear
while soluble sulfate is depleted (left side of Fig. 6.1). Methane accumulation
increases exponentially in the soil only after sulfate becomes undetectable and
the Mn(II) and Fe(II) levels have stabilized. During the incubation time of
about 40 days, the pH value in the soil solution increased from 6.3 to 7.5 and
acetic acid (Table 3.1) as well as hydrogen gas were produced. These two lat-
ter compounds are common products of fermentation, a microbial metabolic
process that occurs when oxygen levels are very low, resulting in the degra-
dation of humus into simpler organic compounds, especially organic acids,
along with the production of H2 and CO2. The reported concentrations of
acetate (millimolar) and H2 gas (micromolar in the soil solution) are typical

Fe(ll)

NO,

3 - J \a*>~^

2-f I Mn(ll) _

10 20 30 40
Time (days)

Inceptisol

Redox
Sequence

I I

r~\ so i~

1 1

▼

- J\

- 1 \_

rA- V

Fe(ll) _

'J. V

—

/"no: \

TA~. 3

I \

1 ^1

* 1

1 1\

40 60 80
Time (days)

Vertisol

100 120

, — .

~~-^

j.
O

1 1

co 2

1 1 1 L

J3i~

-jrir

-^-~

— ▼ —

-*r~

T -

-— " 1

H 2

rf 1

CH 4

y^tfbw^

^,A

-A ~""""

A/A#A*4A.U-A-A.A

+*-

- A

-A—

, ***

I I

40 60 80
Time (days)

1 00 1 20

Figure 6.1. Temporal reduction sequences for an Inceptisol (left) and a Vertisol
(right). Inceptisol data from Peters, V., and R. Conrad. (1996) Sequential reduction
processes and initiation of CH4 production upon flooding of oxic upland soils. Soil
Biol. Biochem. 28:371-382. Vertisol data from Yao, H., et al. (1999) Effect of soil char-
acteristics on sequential reduction and methane production in sixteen rice paddy soils
from China, the Philippines, and Italy. Biogeochemistry 47:269-295.

146 The Chemistry of Soils

of active fermentation. These fermentation products accumulate during the
early stages of incubation, then are depleted as Mn(II) and Fe(II) levels increase
or methane production commences, suggesting consumption by the microbial
community during these latter stages.

Similar trends occur in the Vertisol (right side of Fig. 6.1), which was
maintained under paddy conditions prior to sampling and inundation. Nitrate
disappears quickly, whereas sulfate is depleted gradually over 2 months, after
Fe(II) has risen to a plateau value. The characteristic increase in pH noted in
the Inceptisol was observed in the Vertisol as well. Acetate levels also followed
the same time trend as seen in the Inceptisol. The time trend of net CO2
production (some of the CO2 produced microbially is subsequently lost by
carbonate precipitation) is remarkably similar to that of Fe(II) production;
this strong visual correlation suggests that coupling of some kind is occurring
between the two processes. Detailed C balance measurements indicated that
the sum total of CO2 and methane produced results in the loss of just 8% of
the initial total organic C in the soil, with 85% of this loss manifest as CO2.
Thus, most of the labile C converted and released was used to produce CO2
accompanying the accumulation of Fe(II) in the soil.

The temporal sequence of chemical reactions in a flooded soil has a
spatial counterpart in sediments that are permanently inundated. Figure 6.2
illustrates this fact with vertical profiles of soluble oxygen, sulfate, methane,

Oxygen saturation (%)

Fe (mol L 1 sediment)

100 20 40 60 80
I I I I

0.05

£ 0.10-

0)
Q

0.15

0.20

"I — I — I — I — I — TH'
100 200 300 400

Sulfate and Methane

(mmol m~ 3 )

Figure 6.2. Spatial reduction sequence in freshwater sediments. Data from Kappler, A.,
et al. (2004) Electron shuttling via humic acids in microbial iron(III) reduction in a
freshwater sediment. FEMS Microbiol. Ecol. 47:85-92.

Oxidation-Reduction Reactions 147

and Fe observed in uncontaminated freshwater sediments sampled from the
bottom of Lake Constance in Germany. Oxygen is depleted over the first few
millimeters of zone A, which has a reported rust-brown color that reflects
the presence of humus and Fe(III) oxide minerals. A green-brown zone B
immediately below zone A is associated with the increase of Fe(II), whereas
the reported black color of zone C, defined chemically by the disappearance
of soluble sulfate, suggests secondary precipitation of Fe(II) sulfides. Layer
D, which has no detectable sulfate, is associated with the increase of signifi-
cant methane concentrations in the pore water. An expected increase in pH,
from 6.8 to 7.3, across the 20-cm depth of the four subsurface zones also was
observed. Horizontal spatial zonation akin to the vertical profile in Figure 6.2
can be seen typically in slowly flowing groundwater that has been contami-
nated by effluent from a contiguous landfill, as illustrated in Figure 6.3 for a
study site in Denmark. After the plume of degradable xenobiotic organic com-
pounds invades the sediments below the water table and is advected by ambient
groundwater, microbial processes create a sequence of irregular regions with
spatial ordering outward from the landfill that reflects the contrast between
the incipient aerobic condition of the groundwater and the highly anaerobic
conditions that develop near the landfill where the plume is most concen-
trated. The spatial ordering is, therefore, just the reverse of that observed with
increasing depth in sediments lying at the bottom of a river or lake, although
the ordering from the tip of the invading plume back toward its landfill source

38
34.
30
26
22

Fill

Distance from landfill (m)
100 200 300 400

-+-

^j 2 3 4

5 6 7 8 9

Water table

xGlay/Silt

V///M

Methanogenic

Sulfate-reducing

Iron/manganese-reducing

Nitrate-reducing

Aerobic/Oxic

Figure 6.3. Spatial reduction sequence in an organic contaminant plume invad-
ing oxic groundwater. Reprinted with permission from Christensen, T. H., et al.
(2000) Characterization of redox conditions in groundwater contaminant plumes.
/. Contamin. Hydrol. 45:165-241.

148 The Chemistry of Soils

mimics the spatial sequence in bottom sediments and the temporal sequence
in flooded soils.

Detailed microbiological studies of the sequences and profiles depicted
variously in figures 6.1 to 6.3 have provided important insights regarding the
causes of the characteristic ordering. For example, addition of nitrate to a soil
largely depleted of labile humus by a prior long incubation under anaerobic
conditions slightly inhibits the production of soluble Fe, but severely inhibits
the disappearance of soluble sulfate and the production of methane. These
effects, however, are vitiated after fermentation products, such as H2 gas or
acetic acid, are added to the soil. Similarly, addition of ferrihydrite particles
(Section 2.4) to a soil low in labile humus suppresses the loss of soluble sulfate
and slows the production of methane, and addition of soluble sulfate inhibits
methane production — but these effects also can be reversed by supplying fer-
mentation products, especially H2 gas. Two related overall conclusions can
be drawn from these kinds of observations: (1) chemical reactions occurring
earlier in the sequence can inhibit those that come later and (2) significant
competition for labile humus or microbial fermentation products exists that
favors the chemical reactions occurring earlier in the sequence. These con-
clusions in turn suggest that closer examination of the chemical reactions in
the sequence will reveal the operation of general principles underlying the
observed biogeochemistry of flooded soils. Evidently, competitive microbial
intervention in this biogeochemistry is reflected primarily by the extent to
which labile humus or the products of fermentation are depleted as they
become consumed. This latter inference is in fact borne out by reports of H2
gas, with a residence time in soils that is very short (on the order of minutes),
being driven to much lower concentrations in the soil solution by the produc-
tion of soluble Fe than, for example, by methane production, thus indicating
that H2-consuming microbes associated with chemical reactions that occur
earlier in the sequence operate much more efficiently than those associated
with reactions that occur later on.

6.2 Redox Reactions

An oxidation-reduction (or redox) reaction is a chemical reaction in which elec-
trons are transferred completely from one species to another. The chemical
species that donates electrons in this charge transfer process is called a reduc-
tant, whereas the one accepting electrons is called an oxidant. For example, in
the reductive dissolution reaction

FeOOH(s) + 3 H+ + e" = Fe 2+ + 2 H 2 0(£) (6.1)

the solid phase, goethite (Table 2.5 and Fig. 2.11), on the left side is the oxidant
that accepts an electron (e _ ) and reacts with protons to form the soluble
species Fe 2+ on the right side. As written, Eq. 6.1 is a reduction half-reaction, in
which an electron in aqueous solution serves as one of the reactants. This latter

Oxidation-Reduction Reactions 149

species, like the proton in aqueous solution, is understood in a formal sense
to participate in charge transfer processes. The overall redox reaction always
must be the combination of two reduction half-reactions, such that the species
e _ does not appear explicitly. Equation 6.1, for example, could be combined
(coupled) with the reverse of a half-reaction in which CO2 is transformed to
acetate:

l - C0 2 (g) + ? - H+ + e~ = j CH3CO- + l - H 2 (I) (6.2)

to cancel the aqueous electron and represent the reductive dissolution of
goethite coupled to the oxidation of acetate, CH^CO^ - , which serves as a
reductant:

FeOOH(s) + - CH3CO7 H H+

8 2 8

= Fe 2+ + - C0 2 (g) + 7 - H 2 (£) (6.3)

4 4

Redox reactions can be described in terms of thermodynamic equilibrium
constants analogously to the approach used in Chapter 5 for mineral dissolu-
tion reactions. The only new feature is the need to account for electron transfer.
This is done by associating oxidation numbers with oxidants and reductants,
while being careful to balance the overall redox reaction in terms of reduction
half-reactions, as explained in Special Topic 4 at the end of this chapter. A list
of important reduction half-reactions and their thermodynamic equilibrium
constants (at 25 °C) is provided in Table 6.1. These equilibrium constants have
exactly the same meaning as those discussed in Chapters 4 and 5, even though
the reactions to which they refer contain the aqueous electron. The reason for
this is the convention by which the reduction of the proton is defined to have
log K = (the third reaction listed in Table 6.1). Thus, every half-reaction in
Table 6.1 may be combined with the reverse of the proton reduction reaction
to cancel e _ while leaving log K for the half-reaction completely unchanged
numerically. In this sense, each half-reaction in Table 6.1 is equivalent to an
overall redox reaction that couples it to the oxidation of H 2 gas serving as the
reductant.

The log K data in Table 6.1 can be combined in the usual way to calculate
a value of log K for an overall redox reaction. Consider, for example, the
combination of Eqs. 6.1 and 6.2 to produce Eq. 6.3. According to Table 6.1, the
reduction of goethite has log K = 13.34, and the oxidation of acetate has log
K = 1.20. It follows that the reductive dissolution of goethite by acetate has
log K = 13.34 + 1.20 = 14.54. This equilibrium constant can be expressed in
terms of activities related to Eq. 6.3:

K= (^ + )(CQ 2 )MH 2 OH i=1Ql , 54 (64)

(FeOOH) (H+) 8 (CH 3 CO~) 8

150 The Chemistry of Soils

Table 6.1

Some important reduction half-reactions (25°C).

Reduction half-reaction log K

i0 2 (g)+H++e- = ±H 2 0(£)

\ 2 (g) + H+ + e- = \ H 2 2

H+ + e" = \ H 2 (g) 0.00

|NO" + |H++e- = i NO (g) + | H 2 (€) 16.15

4 ^2 \h) -r 12 ^4 ^ 12 " ^ c -12 ^'^"2'

i C0 2 (g) + H+ + e- = 24- C 6 H 12 6 + I H 2 (£)
j CQ 2 (g) + H+ + e~ = \ CH 4 (g) + i H 2 Q (I)

20.75
11.50

14.15
18.90

= |H 2 (g)

, . -f H++e- = iNO(g) + § H 2 0(<)

i NO" + H+ + e- = \ NO" + i H z O (£)

\ NO" + | H+ + e- = \ N 2 (g) + | H z O (/)

\ NO" + f H+ + e- = i N 2 (g) + f H 2 (£) 21.05

\ NO" + | H+ + e- = \ NH+ + | H 2 (£) 14.90

Mn 3 + + e- = Mn 2 + 25.50

MnOOH(s) +3H++e-= Mn 2 ++2H 2 0(£)

i Mn 3 4 (s) + 4 H+ + e- = | Mn 2 + + 2 H 2 (I)

\ Mn0 2 (s) + 2 H+ + e- = \ Mn 2 + + H 2 (£)

\ Mn0 2 (s) + i C0 2 (g) + H+ + e" = \ M11CO3 (s) + ±H 2 (I)

Fe 3 + + e" = Fe 2 +

\ Fe 2 + + e- = \ Fe (s)

Fe(OH) 3 (s) + 3H++ e" = Fe 2 ++3H 2 0(€)

FeOOH(s) + 3H++ e" = Fe 2 ++2H 2 0(£)

\ Fe 3 4 (s) + 4 H+ + e- = | Fe 2 + + 2 H 2 (£)

\ Fe 2 3 (s) + 3 H+ + e- = Fe 2 + + § H z O (I)

\ SO 2 " + | H+ + e- = \ S 2 2 - + | H 2 (I)

I SO 2 " + | H+ + e- = i HS- + i H 2 (£)

| S0 2 - + | H+ + e- = | H 2 S+| H 2 0(£) 5.13

| C0 2 (g) + ±H+ + e" = \ CHO- -5.22

| CO z (g) + I H+ + e- = ± C 2 H 3 2 - + I H z O (£)

M C0 2 ( g ) + | H+ + e- = i C 6 H 5 COO- + | H 2 (I)

\ C0 2 (g) + i NH+ + {i H+ + e- = i C 3 H 4 2 NH 3 + I H 2 (/)

25.36
30.68
21.82
18.00
13.00
-7.93
17.14
13.34
18.16
12.96
4.85
4.25

1.20
1.76
0.84
0.20
2.86

If the activities of goethite and water are set equal to 1.0, and the usual expres-
sions for the activities of C02(g) and H + are used (Section 5.5), then Eq. 6.4
can be written in the form

(Fe 2+ ) P^ 02 1o¥p h / (CH3CO-) * = 10 14 - 54 (6.5)

Oxidation-Reduction Reactions 151

ChoosingpH 6 andaC02 pressure of 10 atm as typical values, one reduces

this equation to the simpler expression

' ' - 10 2 - 67 (6.6)

(CH 3 CO~) !

Equation 6.6 leads to the conclusion that the equilibrium state of the redox
reaction in Eq. 6.3 requires the activity of Fe + in the soil solution to be
more than 460 times greater than the eighth root of the activity of acetate
in the soil solution. For example, if (Fe 2+ ) = 10 -6 , then Eq. 6.6 predicts
(CH^CO^ - ) ~ 10 . This result shows that, at equilibrium, acetate would be
rather well oxidized to CO2 by the reductive dissolution of goethite.

The reduction half-reactions in Table 6.1 also can be used individually
to predict ranges of pH and other log activity variables over which one redox
species or another predominates. Nearly all reduction half- reactions are special
cases of the generic equation

mA 0X + nH+ + e" = pA red + qH 2 (£) (6.7)

where A is a chemical species in any phase [e.g., CC>2(g) or Fe + ] and "ox" or
"red" designates oxidant or reductant respectively. The equilibrium constant
for the generic half-reaction is

K= (Ared) ; (H ^\ (6.8)

(A ox ) m (H+) n (e-)

This equation can be rearranged, for example, to provide an expression for
pH in terms of other log activity variables. The species A ox and A re d, whose
activities are related in this way through electron transfer and Eq. 6.8, are
termed a redox couple. In Eqs. 6.1 and 6.2, for example, the redox couples are
goethite/Fe 2+ and CC>2/acetate respectively.

Application of Eq. 6.8 to soils requires an interpretation of (e _ ), the
activity of an aqueous electron. This can be accomplished by following the
paradigm already well established for the aqueous proton. Soil acidity is
expressed quantitatively by the negative common logarithm of the proton
activity, the pH value. Similarly, soil "oxidizability" can be expressed by the
negative common logarithm of the electron activity, the pE value:

pE=-log(e-) (6.9)

Large values of pE favor the existence of electron-poor species (i.e., oxidants),
just as large values of pH favor the existence of proton-poor species (i.e., bases).
Small values of pE favor electron-rich species, reductants, just as small values
of pH favor proton-rich species, acids. Unlike pH, however, pE can take on
negative values. This difference results from the separate conventions used to
define log K for acid-base and redox reactions (Table 6.2). In soils, pE ranges

152 The Chemistry of Soils

Table 6.2

Comparing pE

anc

pH.

Species

Reaction

Predominance

Condition

Acid

Donates H +

LowpH

Acidic

Base

Accepts H+

High pH

Basic

Reductant

Donates e~

LowpE

Reducing

Oxidant

Accepts e~

High pE

Oxidizing

Reference reactions

H z O(€) + H+

= H 3

log

Acid-base

H+ + e- = I

H 2 (j

;)

log

Redox

from around +13.0 to less than —6.0. At circumneutral pH, this range can be
partitioned broadly into oxic (pE > +2), suboxic (+12 > pE > +2), and
anoxic (pE < +2) zones.

These definitions are motivated after rewriting Eq. 6.8 as an expression
for pE [assuming (H2O) = 1.0]:

pE = log K + log

(Aqx)"

(A re d) F

npH

(6.10)

Oxic conditions occur in a soil solution at pH 7 if the partial pressure of
oxygen is greater than about 0.01 atm (about 5% of the atmospheric partial
pressure). The corresponding pE value can be calculated by introducing the
oxygen reduction half-reaction (first reaction listed in Table 6.1) into Eq. 6.10,
withA ox = 2 (g) andA red = H 2 0(£):

pE = 20.75 + - log Pq 2 - 7 = 20.75 - 0.5 - 7 = + 13.25

Thus, pE values greater than about 12.0 characterize oxic soils. At pE values less
than +12.0, the partial pressure of oxygen drops below 0.01 atm and anaerobic
conditions obtain.

Suboxic status in a soil at pH 7 can be associated with pE values calculated
for nitrate reduction or for the reductive dissolution of Mn0 2 (s). The latter
reaction, listed in the middle of Table 6.1, yields the pE expression [assuming
(Mn0 2 (s)) = 1.0]

pE = 21.82 - - log (Mn 2+ ) - 14 = 7.82 log (Mn 2+ ) ss + 8.8

if (Mn 2+ ) ~ 10 -2 . Similarly, the reduction of nitrate to form ammonium ions
(eighth reaction listed in Table 6.1) yields the pE expression

pE = 14.90 + - log

(NO3-)

(NH|)

5.75 Rs + 6.15,

if the pE value for (N0 3 ) = (NH^~) is taken as a threshold.

Oxidation-Reduction Reactions 153

Anoxic soils are characterized by the reduction of ferric iron and sulfate
along with the production of methane. Returning to Eq. 6.1 as an example,
one finds the pE expression

pE = 13.34 - log(Fe 2+ ) - 21.0 = -7.66 - log(Fe 2+ ) ss -4.66

if (Fe + ) ~ 10 , an activity typical of a flooded soil. Note that the reductive
dissolution of Fe(OH)3(s), a poorly crystalline solid phase, would yield a pE
value near —2 under the same conditions, thus illustrating the need for broad
ranges of pE to delineate oxic, suboxic, and anoxic conditions.

Nitrate reduction to form ammonium ions is an example that is useful
for emphasizing another important concept about redox reactions. For a fixed
pE value, an increase in ammonium ion activity relative to that of nitrate
requires lowering the pH value, a trend that also can be deduced directly
from Eq. 6.10 by considering decreases in [(A ox ) m /(A re d) p ]- The formation
of reductants almost always results in proton consumption and, therefore, an
increase in pH. Thus each reduction half-reaction in Table 6.1 represents a
mechanism by which free protons can be removed from the soil solution.
Reduction is therefore an important way by which soil acidity can be decreased.
Conversely, oxidation can create free protons and increase soil acidity.

It is also very important to keep in mind that the data in Table 6.1 imply
that certain redox reactions can occur in soils, but not that they will occur.
A chemical reaction that is favored by a large value of log K is not neces-
sarily favored kinetically This fact is especially applicable to redox reactions
because they are often extremely slow, and because reduction and oxidation
half-reactions often do not couple well to each other. For example, the cou-
pling of the half-reaction for 02(g) reduction with that for acetate oxidation
leads to a log K value of 22.0 for the overall redox reaction:

l - 2 (g) + l - C 2 H 3 2 - + l - H+ = X - C0 2 (g) + -j- U 2 (I) (6.11)

For a soil solution that is in equilibrium with the atmosphere (Po 2 = 0.21
atm), the value of log K just given predicts complete oxidation of acetate at
any pH value. But this prediction is contradicted by the observed persistence
of dissolved acetate and other components of humus in soil solutions under
surface terrestrial conditions. A rather similar example can be developed by
considering N 2 (g) oxidation coupled to 2 (g) reduction, leading to the con-
clusion that, under the current oxic conditions at the earth's surface, the oceans
should have become nitrate solutions.

The typically sluggish nature of redox kinetics implies that catalysis is
required if redox reactions are to equilibrate on timescales comparable with
the life cycles of the biota. In soils, the catalysis of redox reactions is effected by
microbial organisms and, to a lesser extent, mineral surfaces. In the presence
of the appropriate microbial species, a reduction half-reaction can proceed
quickly enough in a soil to produce activity values of the reactants and products

154 The Chemistry of Soils

that largely agree with equilibrium predictions. If the reductant thus produced
by the half-reaction accumulates outside the microbial cell, catalysis is termed
dissimilatory; otherwise, it is assimilatory. For example, nitrate reduction by
bacteria to yield ammonium ions that are metabolized to form amino acids,
such as glutamic and aspartic acid (Table 3.2), is assimilatory, whereas denitri-
fication is dissimilatory. Of course, these possibilities are dependent entirely
on the growth and ecological interactions of the soil microbial community
and the degree to which the products of biochemical reactions can diffuse
readily in the soil solution. In some cases, redox reactions will be controlled
by the highly localized and variable dynamics of an open biological system,
with the result that redox speciation at best will correspond to local conditions
of partial equilibrium. In other cases, including often the important one of
the flooded soil, redox reactions will be controlled by the behavior of a closed
chemical system that is catalyzed effectively by bacteria and mineral surfaces,
for which an equilibrium description is apt. Regardless of which of these two
extremes is the more appropriate to characterize redox reactions, the role of
organisms (and mineral surfaces) deals only with the kinetics aspect of redox.
If a redox reaction is not favored by a positive log K, microbial intervention
cannot change that fact.

6.3 The Redox Ladder

A redox ladder is a vertical line marked off with "rungs" that are occupied by
redox couples, with the oxidant on the left and the reductant on the right.
This vertical line is a coordinate axis labeled by pE values calculated using
Eq. 6.10 (or an equivalent expression) for a fixed pH value, usually pH 7.0.
Construction of the "ladder" is based on three conventional rules.

Rule 1: Each redox couple on the ladder must be related by a reduction half-
reaction in which the stoichiometric coefficient of e _ is 1.0. If this half-
reaction has the generic form in Eq. 6.7, then pE values are calculated
with Eq. 6.10 after fixing the pH value and setting (H 2 0(£)) = 1.0.

Rule 2: If the oxidant and reductant are in the same phase, then (A ox ) and
(A rec j) are each set equal to 1.0, yielding a simplified equation for pE
at a given pH:

pE = logK-npH (6.12)

where K is the thermodynamic equilibrium constant for the reduc-
tion half-reaction transforming the oxidant into the reductant in a
redox couple and n is the stoichiometric coefficient of H + in this
half-reaction.

Oxidation-Reduction Reactions 155

Example: The reduction of sulfate to form bisulfide is described by the
half-reaction (Table 6.1)

SO;;" + - H+ + e"

- HS~ + - H 2 (£) (6.13)

8 2

for which logK = 4.25 at 25 °C. Placement of the redox couple
S0 4 _ /HS _ , on the ladder is therefore at pE = —3.63, if pH = 7
(Fig. 6.4).

Comment: If the activities of the oxidant and reductant are known,
they may be used to calculate pE according to Eq. 6.10. For example,
(S0 4 ~) = 10 -3 and (HS~) = 10 -4 could occur in a fresh ground-
water sample, leading to pE = —3.50 at pH 7. Note the typical rather
small effect of this correction on the pE value.

15 OxRed 15

°2

Fe 3+

Fe 2+ H,0

N0 3
10

N 2
1f)

Mn0 2

MnOOH

Mn"'

°2

NOi

NO" H 2 2

N0 3 ]

NH 4 +

FeOH

FeOH +

Fe(OH) 3

CO„

so;

Fe^

HS"

— FeOOH Fe 2+

-5

CO„

CH,

CO^

CO,

Fe^

-10_
PE

C 6 H 5 COO"

Fe'
.-10

Figure 6.4. A redox ladder constructed for pH 7. Auxiliary conditions imposed on
redox species activities are discussed in the text.

156 The Chemistry of Soils

Rule 3: If either the oxidant or the reductant is in a gaseous or a solid phase,
the gas-phase species activity is equated to the partial pressure in units
of atmospheres and the solid-phase species activity is set equal to
1.0. The activity of the remaining, aqueous-phase species in the redox
couple is equated to its concentration in moles per cubic decime-
ter (Section 4.5). Suitable values of the partial pressure or aqueous
concentration are used in calculating pE with Eq. 6.10.

Example: Calculations illustrating Rule 3 were presented in Section 6.2
for the reduction of 02(g) and the reductive dissolution of Mn02(s).
The resulting pE values are also depicted in Figure 6.4. Another exam-
ple is provided by the reduction of C02(g) to form glucose, as occurs
in photosynthesis (Table 6.1):

\ C0 2 (g) + H+ + e" = i- C 6 H 12 6 + \ H 2 (I)

4 v ' 24 4

logK=-0.20 (6.14a)

If Pco 2 = 10 -2 atm and (C^AyiO^) ~ 5 x 10 -4 (based on a glucose
concentration of 0.5 mol m ), then at pH 7.0,

pE = - 0.20 + - Pco 2 - — log (C 6 Hi 2 6 ) - pH

= - 0.20 - 0.50 + 0.14 - 7 = -7.56

This very low pE value is typical of reduction half-reactions involving
biomolecules. Note again the small effect of the redox couple activities
on the pE value.

Perhaps the most important application of the redox ladder is its use to
establish which member of a redox couple is favored (i.e., thermodynamically
stable) under given conditions in a soil. This application is initiated by deter-
mining where a soil is poised with respect to pE. Poising is to pE what buffering
is to pH (Section 3.3 and Problem 8 in Chapter 3). Thus, a well-poised soil
resists changes in pE, just as a well-buffered soil resists changes in pH. Indeed,
pE "poisers" are available with which to calibrate pE electrodes, just as pH
buffers are available with which to calibrate pH electrodes. For example, the
half-reaction

p-benzoquinone + H + e _ = - hydroquinone logK = 11.83 (6.15)

is often used for calibration, with the poised suboxic pE value being given by
pE = 11.83 — pH, according to Eq. 6.12. [Benzoquinone comprises a benzene
ring with a pair of carbonyl (C = O) substituents. If one of the carbonyls is
converted to a C — OH group, the resultant compound is termed semiquinone
and, if both carbonyls are converted, it is termed hydroquinone. This latter

Oxidation-Reduction Reactions 157

compound, a powerful reductant, differs from catechol (Section 3.1) in having
its two OH substituents lie along a single axis of symmetry of the benzene ring
instead of being adjacent to one another on the ring.]

In soils, the most important redox-active elements are H, C, N, O, S, Mn,
and Fe, with the addition of Cr, Cu, As, Se, Ag, Pb, U, and Pu for contaminated
environments. Poising by a reduction half-reaction involving one of these
chemical elements depends on its relative abundance as an oxidant species in
a soil. For example, abundant 02(g) in a soil atmosphere implies poising of
the soil by the first reduction half-reaction listed in Table 6.1, with the poised
pE value then given by

pE = 20.75 + \ log Po 2 - pH (6.16a)

according to Eq. 6.10. If Po 2 drops well below its nominal atmospheric value
(0.21 atm), 02(g) no longer will be sufficient to poise pE and the reduction
half- reactions of nitrate become potential candidates for poising pE. For exam-
ple, nitrate reduction, described by the two reactions in Table 6.1 with aqueous
ions as products, might poise pE in the suboxic range (Fig. 6.4) if nitrate
is abundant. Otherwise, poising by the reductive dissolution of Mn02(s)
would be expected, because Mn is a relatively abundant metal element in
soils (Table 1.2), with the poised pE value given by

pE = 21.82 log (Mn 2+ ) - 2 pH (6.16b)

Note that the other solid-phase oxidant species of Mn listed in Table 6.1
are thermodynamically unfavored relative to Mn02(s). If the reverse of the
reduction half-reaction for Mn02(s) is added to those for the other two oxi-
dant solid phases, the resulting log K > 0. Indeed, manganite (y-MnOOH),
a typical product of abiotic air oxidation of soluble Mn(II), disproportionates
into Mn0 2 (s) and Mn 2+ :

4- 1 1 9 +

MnOOH(s) + H+ = - Mn0 2 (s) + - Mn 2+

2 2

+ H 2 0(£) log K = 3.54 (6.17)

Nonetheless, either of the solid phases, manganite or hausmannite (M^O^,
may be found in soils as metastable species. [Note also that various species of
Mn02(s) exist (polymorphs). Equation 6.16b applies to that most resembling
birnessite (Section 2.4). If the most stable species (pyrolusite, |3-Mn02) were
considered instead, log K would be changed to 20.56.]

Under anoxic conditions, reduction half-reactions involving oxidant
species of Fe, S, or C (if the reductant product is a biomolecule) can poise
pE in a soil:

pE = 17.14 - log(Fe 2+ ) - 3pH (6.16c)

158 The Chemistry of Soils

if the oxidant is Fe(OH)3(s),

pE = 4.25 + - log

if the oxidant is soluble sulfate, or

(son

(MS")

-pH

pE = 2.86 + - log

Pco 2
LPchJ

(6.16d)

(6.16e)

if methanogenic bacteria are active. At a given pH value, the pE values for
the reductive dissolution of Fe(OH)3(s), sulfate reduction, and methane
production lie successively lower on the redox ladder (Fig. 6.4). To the
extent that the pE values are well-separated on the ladder, they are characteris-
tic of the reduction half-reactions from which they are derived. In recognition
of this possibility and the ubiquity of dissimilatory microbial catalysis of soil
redox reactions, the half- reactions represented by Eq. 6.16 are called terminal
electron-accepting processes (TEAPs). In microbiological terms, one portrays
TEAPs as key chemical reactions governing microbial respiration and portrays
the bacteria involved as oxygen-, nitrate-, or iron-respiring, and so on. Thus,
pE in soils is pictured as poised by TEAPs involving the abundant oxidant
species of the elements O, N, Mn, Fe, S, or C. In polluted soils, TEAPs involv-
ing the eight potentially hazardous elements mentioned earlier also may poise
pE if abundant oxidant species of them are present.

How is the poising of a soil pE value quantified? The corresponding ques-
tion of how the buffering of a soil pH value is quantified has a simple answer
in terms of pH measurement using a glass electrode — a technological advance
perfected by Arnold Beckman more than 75 years ago (see Special Topic 5 at
the end of this chapter). Unfortunately, an equivalent success has not occurred
in the development of an electrochemical method to measure pE. To be sure,
an electrode potential (Eh, in units of volts) can be defined formally in terms
of pE:

In 10 pE = 0.05916 pE (25 °C)

(6.18)

where R, the molar gas constant; T, the absolute temperature (298.15 K at
25 °C); and F, the Faraday constant; are defined in the Appendix. Equation
6.18 is a purely formal relationship amounting to a transformation of units.
In practice, electrochemical measurements of Eh are subject to numerous
interferences, notably the lack of thermodynamic equilibrium between oxidant
and reductant in a redox couple (i.e., the ambiguity inherent to interpreting
a voltage read at zero net current as the unique signature of a single redox
couple at equilibrium) and an anomalous selectivity for Fe(III)/Fe(II) redox
couples. Measured values of Eh obtained by a suitably calibrated electrode
thus have only a qualitative significance in soil solutions. A similar conclusion

Oxidation-Reduction Reactions 159

can be drawn concerning the use of redox indicators, which, like pH indicators,
change color at certain pE values. These compounds can be adsorbed by soil
particles or complexed by metal cations, and their colors are pH sensitive.

The most common method used to measure pE in soils and aquifers
is quantitation of redox couples. For example, C>2(aq) concentrations can
be measured to determine whether poising by O2 reduction is occurring.
If these concentrations are below about 15 mmol m -3 (corresponding to a
partial pressure of about 0.01 atm), then O2 reduction cannot be the TEAP
that poises soil pE. Similarly, nitrate concentrations below about 3 mmol
m -3 would eliminate nitrate reduction as a candidate for the TEAP-poising
pE. On the other hand, Mn(II) or Fe(II) concentrations exceeding about
100 mmol m -3 may signal pE poising by the reductive dissolution of Mn(IV)
or Fe(III) oxy(hydr) oxides respectively. Depletion of soluble sulfate below
100 mmol m -3 would tend to rule out sulfate reduction as the pE-poising
TEAP, whereas methane concentrations above about 50 mmol m -3 point to
methane production as a poiser. Supporting microbiological evidence for large
numbers of the bacteria utilizing a proposed pE-poising TEAP is a helpful
adjunct to quantitation. As implied in Figures 6.1 to 6.3, however, overlapping
TEAPs identified by quantitation can obfuscate this approach.

6.4 Exploring the Redox Ladder

The redoxladder in Figure 6.4 shows the O2/H2O couple on the top "rung" and
the CO2/C6H12O6 couple on a very low rung. Oxygen gas in the atmosphere
constitutes an enormous oxidant reservoir, whereas humus and the biota,
loosely represented by glucose, constitute an equally important reservoir of
organic reductants. As noted in Section 6.2, large values of pE favor oxidants
like 02(g), whereas small (e.g., negative) values of pE favor reductants like
glucose and other organic molecules. In a redox reaction, two reduction half-
reactions are combined after one of them is reversed, such that the resulting
overall reaction does not exhibit e _ as a participant. How does one determine
which of the two half-reactions to reverse? When two half-reactions are cou-
pled, electron transfer always must be from low pE (electron rich) on the redox
ladder to high pE (electron poor) on the ladder. Thus, in the current example,
the half-reaction involving glucose is the one to be reversed, making glucose a
reactant and yielding the overall redox reaction

7 O2 (g) + - 1 - C 6 H 12 6 = - C0 2 (g) + \ H 2 (I) (6.19)

4 v ' 24 4 v ' 4

which loosely depicts the aerobic oxidation of humus, akin to the reaction in
Eq. 6.11. Equation 6.19 maybe interpreted as an electron titration of humus,
analogous to the proton titration of humus described in Section 3.3. Oxidant
[02(g)] reacts with reductant C to yield oxidant C and water, just as base
reacts with acidic C to yield basic C and water (Table 6.2). Out of this analogy,

160 The Chemistry of Soils

humus emerges as an important terrestrial reservoir of both reactive protons
and reactive electrons, with the capability, therefore, of both buffering soil
pH and poising soil pE. Whether this potential is realized, of course, depends
on the relative abundance of competing inorganic buffers and poisers, and
the ability of the soil microbial community to catalyze the relevant electron
transfer reactions.

Suppose, for example, that soil pE is poised by the reductive dissolu-
tion of MnC>2(s) coupled with the oxidation of humus (the pE value for the
MnC>2/Mn + couple lies above those for C02/organic molecule couples in
Fig. 6.4). Thus, if (Mn 2+ ) = 10 -2 and pH = 7, pE is poised at +8.8, according
to Eq. 6.16b (Fig. 6.4). Above this rung on the redox ladder are redox couples
with oxidant members that are sustained in equilibrium with the reductant
members only at higher pE values. If pE drops below the rung for a given
redox couple, the oxidant member is destabilized and the reductant member
becomes highly favored. For example, if pE = 8.8 is introduced into Eq. 6.16a
at pH 7, Po 2 ~ 10 atm and 02(g) has effectively disappeared in favor of
H20(£). On the other hand, just the opposite trend applies to redox couples
perched on rungs below that at pE = +8.8. For them, it is the reductant
member that is destabilized, because these redox couples are sustainable at
equilibrium only when pE drops to lower values. If pE = 8.8 is introduced
into Eq. 6.16c, for example, the resulting Fe + activity is only about 2 x 10 .
The general conclusion to be drawn here is the following:

IfpE is poised at a certain value on the redox ladder, the favored species
in all redox couples perched at higher (lower) pE values than the poised
pE is the reductant (oxidant) species in the couples.

It is in this context that the reduction sequences for flooded soils shown in
Figures 6. 1 to 6.3 can be understood and interpreted in terms of pE descending
the redox ladder. Electrons are produced in copious amounts by the micro-
bially mediated oxidation of both humus (e.g., the reverse of the reaction in
Eq. 6.14) and the reductants produced in fermentation processes [e.g., organic
acids and H2 (g) ] . As electrons accumulate and the pE value of the soil solution
drops below +12.0, enough e _ become available to reduce 02(g) to H20(£).
Below pE 5, oxygen is not stable in neutral soils. Above pE 5, it is consumed in
the respiration processes of aerobic microorganisms. As the pE value decreases
further, electrons become available to reduce NO^~. This reduction is catalyzed
by nitrate respiration (i.e., NO^~ serving as a biochemical electron acceptor like
O2) involving bacteria that ultimately excrete NO^, N2, N2O, NO, or NH^f".

As soil pE value drops into the range 9 to 5, electrons become plentiful
enough to support the reduction of Mn(IV) in solid phases. The reductive
dissolution of Fe(III) minerals does not occur until O2 and NO^~ are depleted,
but Mn reduction can be initiated in the presence of nitrate. As the pE value
decreases below +2, a neutral soil becomes anoxic and, when pE < 0, electrons
are available for sulfate reduction catalyzed by a variety of anaerobic bacteria.

Oxidation-Reduction Reactions 161

Typical products in aqueous solution are H2S, bisulfide (HS _ ), or thiosulfate
(S20^~) ions. Methane production ensues for pE < —4, a value characteristic
of fermentation processes.

The chemical sequence for the reduction of O, N, Mn, Fe, and S or for
methane production induced by changes in pE is also an ecological sequence
for the biological catalysts that mediate these reactions. Aerobic microorgan-
isms that utilize O2 to oxidize organic matter do not function below pE 5.
Nitrate-reducing bacteria thrive in the pE range between +10 and 0, for the
most part. Sulfate-reducing bacteria do not do well at pE values above +2.
These examples show that the redox ladder portrays domains of stability for
both chemical and microbial species in soils.

It is noteworthy that Fe(III)/Fe(II) redox couples span the entire length
of the redox ladder in Figure 6.4-some 22 orders of magnitude in electron
activity! Five rungs are occupied by these couples, beginning with the free-
ion species at pE = + 13.0 and ending with the Fe 2+ /Fe° couple at pE =
—7.93 + j log(Fe + ). The redox couples perched between these two extremes
comprise complexed species of the two free cations Fe 3+ and Fe 2+ . These
couples are associated with log K values in Table 6.1 that reflect the influence
of complex formation on the two free-ion species. If L is a ligand that forms
a complex with Fe 3+ and Fe 2+ , then the reduction half-reaction that relates
the oxidant FeL/ 3- ' to the reductant FeLA 2- ' is the sum of three component
reactions:

Fe 3+ + e" = Fe 2+

logK = +13.0

FeL( 3 "^ = Fe 3+ + i/"

-logc

Fe2+ + I 1 ' = FeL< 2 -^

logK£

FeL (3_£) + e" = FeL (2 ~

■Q

logK

where Kl is the thermodynamic equilibrium constant describing the formation
of an FeL complex. The overall equilibrium constant for the FeLA 3 ' /VtV- 2 ~ '
couple is then log K = 13.0 — log K™ + log K L '. It is apparent that the
associated pE value

pE L = 13.0 - log KJ" + log K L ' (6.20)

will decrease if, as is almost always true, the stronger complex is formed by
Fe 3+ (i.e., K^ > K.'{). Thus, for example, if L e ~ = OH _ ,logKo H = 11.8,
log Kq H = 4.6, and pEoH = +5.8 — a drop by more than seven orders of
magnitude in electron activity (Fig. 6.4). A very similar argument can be con-
structed to account for the placement of the Fe(OH)3/Fe 2+ and FeOOH/Fe 2+
couples, because the two Fe(III) solid phases are formed by reacting Fe + with
H2O as a ligand that hydrolyzes to yield the solid-phase product and pro-
tons, thus producing an overall reaction of the form in Eq. 6.7. Clearly, these

162 The Chemistry of Soils

solid-phase products are stronger "complexes" than the solvation complex of
Fe . The line of reasoning presented is quite general, applying as well to the
Mn(IV)/Mn(II) and Mn(III)/Mn(II) couples. Indeed, Table 6.1 shows that
pE = 25.5 for the Mn 3+ /Mn 2+ couple, whereas MnOOH/Mn 2+ is perched at
pE = 4.40 — log(Mn + ) at pH 7 — a drop of about 19 orders of magnitude in
(e _ )if (Mn 2+ ) Rs 10" 2 .

The Fe 2+ /Fe° couple perched at the bottom of the redox ladder cannot
be interpreted as an effect of complexation. This couple involves "zero-valent
iron," Fe(s), which, from the point of view of redox reactions, is quite analogous
to "zero-valent carbon," as represented, for example, by glucose. This analogy
is more transparent if the reduction half-reaction for goethite/Fe 2+ is added
to that for Fe 2+ /Fe° so as to cancel Fe 2+ and maintain the stoichiometric
coefficient of e _ as 1.0:

1 +12,

- FeOOH (s) + H+ + e" = - Fe (s) + - H 2 (£) log K = -0.84

(6.14b)

which should be compared with Eq. 6.14a. Both half-reactions now span
the full range of positive oxidation numbers for C and Fe with remark-
ably similar log K values, indicating the oxidant to be the favored species
thermodynamically.

The reverse of the reaction in Eq. 6. 14a is respiration, but might be termed
carbon corrosion in the spirit of the reverse of the reaction in Eq. 6.14b. Both
carbon corrosion and the corrosion of iron are spontaneous processes, ther-
modynamically speaking. The two couples CO2/C6H12O6 and FeOOH/Fe
occupy nearly the same place on the redox ladder at any pH value. The
very low pE values at which they are perched ensures that poising a system
with their half-reactions will favor reduced species of virtually every redox-
active element (i.e., the reverse reactions will provide a flood of electrons
to transform oxidants into reductants if suitable catalysis is available). That
this contingency in the case of C has been exploited in the life cycles of soil
microorganisms is well-known. That in the case of Fe it provides a means to
convert any hazardous element into a reduced species that may be innocuous
has, however, only recently been exploited in the design of soil remediation
schemes.

6.5 pE-pH Diagrams

A pE-pH diagram is a predominance diagram (Section 5.4) in which electron
activity is the dependent activity variable chosen to plot against pH. Thus
the pE value plays the same role as the value of log (Si (OH) 4 J in Figure 5.5.
The construction of a pE— pH diagram is, accordingly, another example of the
construction of a predominance diagram. Differences come because of redox
reactions involving only aqueous species and because of the interpretation of

Oxidation-Reduction Reactions 163

the diagram, which is in terms of redox species instead of solid phases alone.
The steps in constructing a pE-pH diagram are summarized as follows:

1. Establish a set of redox species and obtain values of log K for all possible
reactions between the species.

2. Unless other information is available, set the activities of liquid water and
all solid phases equal to 1.0. Set all gas-phase pressures at values
appropriate to soil conditions.

3. Develop each expression for log K into a pE-pH relation. In one relation
involving an aqueous species and a solid phase wherein a change in
oxidation number is involved, choose a value for the activity of the
aqueous species.

4. In each reaction involving two aqueous species, set the activities of the two
species equal.

The resulting pE-pH diagram is divided into geometric regions with interiors
that are domains of stability of either an aqueous species or a solid phase, and
with boundary lines that are generated by transforming Eq. 6.8 (or another
suitable expression for an equilibrium constant) into pE— pH relationships
like Eq. 6.10. By examining a pE-pH diagram for a chemical element (e.g., Mn
or S), one can predict the redox species expected at equilibrium under oxic,
suboxic, or anoxic conditions in a soil at a given pH value.

To illustrate these concepts, consider a pE-pH diagram for Fe based on
conditions in the Philippines Vertisol with the reduction sequence depicted on
the right in Figure 6.1. First, a suite of redox species is chosen: Fe(OH)3(s), a
poorly crystalline Fe(III) mineral similar to ferrihydrite (Section 2.4) that
the GLO Step Rule (Section 5.2) would favor in flooded soils; FeC03(s),
a carbonate mineral observed in anoxic soils (Section 2.5); and Fe . The
reductive dissolution of Fe(OH)3(s) is listed in Table 6.1 and its associated
pE— pH relationship following the steps just listed appears in Eq. 6.16c. The
dissolution reaction for siderite,

FeC0 3 (s) = Fe 2+ + C0 2 ~ logK so = -10.8 (6.21)

is expressed more conveniently after combining it with Eq. 5.33 and the
bicarbonate dissociation reaction

HCO~ = H+ + CO 2- log K 2 = -10.329

similar to what was done with the calcite dissolution reaction in Section 5.5.
The resulting overall dissolution reaction is

FeC0 3 (s) + 2H+ = Fe 2+ + H 2 0(£) + C0 2 (g) (6.22)

for which log K = -10.8+ 1.466 + 6.352+ 10.329= 7.35 at 25 °C. Note the
similarity to Eq. 5.34, although siderite is less soluble than calcite.

164 The Chemistry of Soils

The final reaction needed to construct a pE-pH diagram is found by
combining the two dissolution reactions just considered:

Fe(OH) 3 (s) + C0 2 (g) + H+ + e" = FeC0 3 (s) + 2H 2 0(£) (6.23)

for which logK = 17.14 - 7.35 = 9.79 at 25 °C. Note the similarity to the
reaction in Table 6.1 relating MnC>2(s) to MnC03(s).

The pE-pH relationships that define the boundary lines in a pE— pH dia-
gram describing the three Fe redox species are then, following Step 2 presented
earlier,

pE = 17.14 - log(Fe 2+ ) - 3pH (6.24a)

= 7.35 - log(Fe 2+ ) - log P C o 2 - 2pH (6.24b)

pE = 9.79 + log P C o 2 - pH (6.24c)

Because Eq. 6.22 is not a reduction half-reaction, it does not involve pE when
its log K is expressed in terms of log activity variables. It will plot as a vertical
line in a pE-pH diagram.

Equation 6.24 cannot be implemented in a pE— pH diagram until fixed
values for (Fe + ) and Pco 2 are selected. Reference to Figure 6.1 indicates
that Pco 2 ^ 0-12 atm after about 100 days of incubation of the Philippines
soil. A measured value of (Fe 2+ ) is not available, but (Fe 2+ ) ~ 2 x 10 -4 is
reasonable for a flooded acidic soil. With these data incorporated, Eq. 6.24
becomes the set of working equations

pE = 20.84 - 3pH (6.25a)

pH = 6.0 (6.25b)

pE = 8.86 - pH (6.25c)

The boundary lines based on Eq. 6.25 are drawn in Figure 6.5. Equation 6.25a
is the boundary between Fe(OH)3(s) and Fe + in respect to predominance of
one redox species or the other. Above the line, pE increases and Fe(OH)3(s)
predominates; below the line, the solid phase dissolves to form Fe 2+ as the
predominant species under the given conditions of Fe + activity and CO2
partial pressure. This change in predominance as pE decreases has important
consequences for the soil solution concentrations of metals like Cu, Zn, or Cd,
and of ligands like F^PO^T or HAs0 4 - . The principal cause of this secondary
phenomenon is the desorption of metals and ligands that occurs when the
adsorbents to which they are bound become unstable and dissolve. Typically,
the metals that are released in this fashion, including Fe, are soon readsorbed
by solids that are stable at low pE (e.g., clay minerals or soil organic matter) and
become exchangeable surface species. Redox-driven surface speciation changes
have an obvious influence on the bioavailability of the chemical elements
involved, particularly phosphorus, arsenic, and selenium.

Oxidation-Reduction Reactions 165

(Fe 2+ ) = 2x 1CT 4

p co 2 = ai2atm

Fe z

Fe(OHUs)

FeCOg(s)

PH
Figure 6.5. A pE-pH diagram for the system Fe(OH) 3 (s), FeC0 3 (s), and Fe 2+ .

At pH 6, however, siderite becomes the predominant Fe(II) species at low
pE under the fixed conditions assumed. The vertical boundary line signaling
this transition in Figure 6.5 is remarkably robust under shifts in the values of
(Fe + ) or Pco 2 - F° r example, if (Fe + ) decreases to 10 , or if Pco 2 decreases
to 10 atm, its atmospheric value, the pH value for siderite precipitation

is increased to about 7.0. Increasing (Fe 2+ ) to 10 -3 (the value assumed in
Figure 6.4) decreases the pH value to 5.6. Thus, siderite precipitation can be
expected in a flooded soil as its pH increases from above 5 to above 7 during
the typical reduction sequence, according to Eq. 6.24. The initial pH value in
the Philippines Vertisol was 5.8, reaching 7.0 when the CO2 partial pressure
achieved its plateau (Fig. 6.1). Thus, siderite precipitation in this soil may
have occurred. The initial pE value in the soil was estimated (by Pt electrode)
to be +8, dropping rapidly to and remaining around -0.6 after only a few
days. The initial state of the soil plots comfortably within the Fe(OH)3(s)
field in Figure 6.5, whereas the final state does the same for the FeCC>3(s)
field, irrespective of whether (Fe + ) or Pco 2 mav differ somewhat from their
assumed fixed values.

For Further Reading

Brookins, D. G. (1988) Eh-pH diagrams for geochemistry. Springer- Verlag,
New York. After a careful presentation of the method for their construc-
tion, this book presents typical pE— pH diagrams for all the chemical

166 The Chemistry of Soils

elements of interest in environmental geochemistry. Brookins prefers to
use electrode potential (Eq. 6.18) as a surrogate for pE.

Christensen, T. H., P. L. Berg, S. A. Banwart, R. Jakobsen, G. Heron, and
H.- J. Albrechtsen. (2000) Characterization of redox conditions in
groundwater contaminant plumes. /. Contamin. Hydrol. 45:165. This
masterful review article describes a broad variety of techniques for mea-
suring pE and characterizing the redox-related microbial community in
groundwater-an excellent read to round out the current chapter.

Kirk, G. (2004) The biogeochemistry of submerged soils. Wiley, Chichester, UK.
The eight chapters of this outstanding monograph can be read to gain a
thorough introduction to the chemistry of wetlands soils.

Langmuir,D. (1997) Aqueous environmental geochemistry. Prentice Hall, Upper
Saddle River, NJ. Chapters 1 1 and 12 of this advanced textbook offer
useful applications of the concepts developed in the current chapter to
environmental geochemistry, with special emphasis on iron and sulfur
redox reactions.

Stumm, W., and J. J. Morgan. (1996) Aquatic chemistry. Wiley, New York.
Chapters 8 and 1 1 of this classic advanced textbook provide the most
thorough discussion available of redox reactions in natural water systems,
including issues surrounding the measurement of pE and the mechanistic
underpinnings of redox kinetics.

Problems

The more difficult problems are indicated by an asterisk.

1. Gao et al. [Gao, S., K. K. Tanji, S.C. Scardaci, and A. T Chow (2002) Com-
parison of redox indicators in a paddy soil during rice-growing season
Soil Sci. Soc. Am. J. 66:805.] have investigated the TEAPs that occur over
a 90-day period after flooding in a California Vertisol under paddy rice
cultivation. The principal results obtained are presented in their Figure 4
and their Table 2. Use these data to prepare graphs similar to those in
Figure 6.1 for the "SB-WF" treatment (filled squares in their Figure 4;
columns 1 and 2 in their Table 2). (Hint: Use Table 1.6 to assist in plotting
data for H2 and CH4.)

2. Develop a balanced redox reaction for sulfate reduction to bisulfide
coupled to glucose oxidation to bicarbonate.

3 . Bacteria of the genus Nitrobacter catalyze the oxidation of nitrite to nitrate
using 02(g) as an electron acceptor. Write a balanced overall redox reac-
tion for this process and calculate log K. What will be the concentration
ratio of NO^~ to NO^ when pE = 7 at pH 6?

Oxidation-Reduction Reactions 167

*4. Hydrogenotrophic anaerobes like Paracoccus denitrificans oxidize H2 gas
while catalyzing denitrification to produce N2 gas (penultimate N
half-reaction in Table 6.1).

a. Show that the oxidation of, say, glucose or acetate to yield H2 gas is a
favorable reaction.

b. Show that the reduction of nitrate to N2 gas by the oxidation of H2
gas is a favorable reaction.

c. Show that the oxidation of zero-valent iron to yield H2 gas is a
favorable reaction.

Perform a literature search to determine whether the redox reaction in (c)
can be used to generate the H2 gas required by P. denitrificans in catalyzing
the reaction in (b).

5. The chloride-bearing variety of green rust (Section 2.4) undergoes the
reduction half-reaction

Fe 4 (OH) 8 Cl(s) + 8H+ + e" = 4 Fe 2+ + Cl" + 8 H 2 0(£)

with logK = 42.7 at 25 °C. Place the redox couple, green rust/Fe 2+ , on
the redox ladder in Figure 6.4 using (Cl - ) = 2 x 10 . Compare its
"rung" with those for the other Fe(II)-containing oxide minerals listed in
Table 6.1.

6. The hydroxamate siderophore desferoxamine B (DFOB) complexes
Fe 3+ and Fe 2+ according to the reactions

Fe 3+ + DFOB = Fe(III)DFOB log K s = 30.6
Fe 2+ + DFOB = Fe(II)DFOB log K s = 10.0

Use this information to place the redox couple Fe(III)DFOB/Fe(II)DFOB
on the redox ladder in Figure 6.4. (See Section 3.1 for a discussion of
microbial siderophores.) Explain how complexation by DFOB can be
interpreted as a strategy to stabilize Fe in the +III oxidation state down to
very low pE levels. This strategy on the part of microorganisms prevents
Fe(III) release at sites other than the intended target cell receptor.

7. Develop an expression analogous to Eq. 6.20 to show that precipitation
of Fe + as hematite, goethite, or Fe(OH)3(s) will always decrease pE on
the redox ladder relative to that for the Fe + /Fe + couple.

8. Perchloroethene (PCE; Ci2C=CCi2, top line in Fig. 3.4) is a rela-
tively water-soluble dry-cleaning solvent that has become a ubiquitous
groundwater contaminant because of improper waste disposal practices.
This chlorinated ethene undergoes reductive dechlorination catalyzed by
bacteria to form trichloroethene (TCE; CICH = CCI2), which is also a

168 The Chemistry of Soils

hazardous organic chemical used industrially as a degreasing solvent:

- PCE + - H+ + e" = - TCE + - Cl" log K = 12.18

2 2 2 2 &

The product species TCE then undergoes reductive dechlorination to
form czsl,2-dichloroefhene (cDCE),

- TCE+ - H+ + e" = - cDCE+ - Cl" logK= 11.35

2 2 2 2 &

which itself can be reductively dechlorinated to form monochloroethene
(or VC, vinyl chloride):

- cCDE + - H+ + e" = - VC + - Cl" logK = 9.05

2 2 2 2

Vinyl chloride is, in turn, transformed into relatively harmless ethene
(ETH, H2C = CH2) by this same microbially catalyzed process:

- VC + - H+ + e" = - ETH + - Cl" logK = 8.82

2 2 2 2 &

Prepare a redox ladder for this set of reduction half-reactions under the
assumption that (Cl~) = 2 x 10 . Compare your results with the
principal redox couples depicted in Figure 6.4, then describe the tem-
poral sequence of chlorinated ethenes expected as a plume of PCE is
biodegraded below a water table.

9. Prepare a redox ladder for the hazardous chemical elements Cr, As, and
Se based on the following reduction half-reactions:

1,5, 1 1

- CrO^" + - H+ + e" = - Cr(OH) 3 (s) + - H 2 {£) logK = 21.06

1 3 , 1 n 1

- H 2 AsO~ + - H+ + e" = - As(OH)° + - H 2 Q {£) logK = 10.84

HAsO^" + 2 H+ + e" = - As(OH)^ + H 2 {£) log K = 14.32

1 , , 1

- HAsOl" + 2 H+ + e" = -

2 4 2

1,3, 1 1

- SeOl" + - H+ + e" = - HSeO" + - H 2 {£) logK = 18.19

2 4 2 2 3 2 &

1 5,13

- HSeO" + - H+ + e" = - Se (s) + - H 2 (I) logK = 13.14
4 4 4 4

Assume pH 7.0 and aqueous species concentrations of 1.0 mmol m

-3

! 10. In alkaline, suboxic soils, the important aqueous species of Se are Se0 4
and Se0 3 ~. Given the half- reaction

- SeO^" + H+ + e" = - SeO;" + - H 2 Q (£) logK = 14.55

Oxidation-Reduction Reactions 169

determine whether Se0 3 - can be oxidized to Se0 4 - (the more toxic,
mobile species) through the reduction of Mn(IV). [Hint: Consider pois-
ing of soil pE by the reductive dissolution of MnC^s) and develop
a relationship between (Mn 2+ ) and pH based on pE values for the
Mn0 2 /Mn 2+ and Se0 2 7Se0 2 ~ redox couples.]

11. Over what range of pH will poising by the reductive dissolution of
MnC^s) be favorable to the complete reductive dechlorination of PCE
to ETH as described in Problem 8? Take (Cl~) = 2 x 10 -3 and
(Mn 2+ ) = 10" 2 .

*12. An amended soil containing gypsum (CaSC>4 • 2H2O, Section 5.1) and
siderite (FeC0 3 ) has a C0 2 pressure of 10" 3 atm and (Ca 2+ ) = 10" 3 - 65
in the soil solution. Calculate the pE value at which FeS (K so = 10 )
will precipitate if pH = 8.2. (Log K = 13.92 for the formation of HS _
from S 2_ and a proton.)

13. Discuss the changes in Figure 6.5 that would occur if goethite is the
Fe(III) mineral instead of Fe(OH)3(s), or the activity of Fe + imposed is
increased to 10 -3 .

14. Prepare a pE-pH diagram for the three redox species Mn02(s),
MnC0 3 (s), and Mn 2+ given (Mn 2+ ) = 10" 3 and P C o 2 = 0.12 atm.
Figure 6.5 can be used to guide your work, but shift the pE axis upward by
5 log units, and shift the pH axis to the right by 1 log unit, to acknowledge
the difference between anoxic and suboxic conditions. Follow the steps in
Section 5.5 to introduce Pco 2 as an activity variable.

15. Use the appropriate reactions in Table 6.1 to prepare a pE-pH diagram

for S based on the aqueous species S0 4 , H2S, and HS

Special Topic 4: Balancing Redox Reactions

Redox species differ from other chemical species in that their status as oxidized
or reduced molecular entities must be noted along with their other chemical
properties. The redox status of the atoms in a redox species is quantified
through the concept of oxidation number, a hypothetical valence, denoted by
a positive or negative roman numeral, that is assigned to an atom according
to the following three rules:

1. For a monoatomic species, the oxidation number equals the valence.

2. For a molecule, the sum of oxidation numbers of the constituent atoms
equals the net charge on the molecule expressed in units of the protonic
charge.

170 The Chemistry of Soils

3. For a chemical bond in a molecule, the shareable, bonding electrons are
assigned entirely to the more electron-attracting atom participating in
the bond. If no such difference exists, each atom receives half the
bonding electrons.

These rules can be illustrated by working out the oxidation numbers for
the atoms in the redox species FeOOH, CHO^~,N2, S0 4 ~, and CgH^Og. In
FeOOH, oxygen is more electron attracting than Fe or H and is conventionally
designated O (-II). Thus, oxygen has oxidation number -2. The hydrogen atom
in OH is designated H(I) (oxidation number +1). By Rule 2, the iron atom is
designated Fe(III), because FeOOH has a zero net charge and 3 + 2(— 2) + 1 =
0. (Recall that this notation was used already in Chapter 2 to distinguish ferric
iron from ferrous iron in soil minerals.) A similar computation can be done for
CHO^~, in which oxygen and hydrogen are designated as above and, therefore,
carbon must be designated C(II), because 2 + 2(— 2) + 1 = — 1 = the net
number of protonic charges on the formate anion.

In the case of N2, there is no difference between the two identical atoms
in the molecule, and, by Rule 3, neither one can be assigned all of the bonding
electrons. Because the molecule is neutral, Rule 2 then leads to the designation
N(0) for each constituent N atom. For sulfate, oxygen is again O(-II) and S
must be S(VI), according to Rule 2. Finally, in glucose, C on average must be
C(0) because the designations O(-II) and H(I) lead by themselves to a neutral
C6H12O6 molecule.

Redox reactions obey the same mass and charge balance laws as described
for other chemical reactions in Special Topic 1 at the end of Chapter 1. The
only new feature is the need to account for changes in oxidation number when
charge balance is imposed. Consider, for example, the aerobic weathering of
an olivine to form goethite (Section 2.2). The essential characteristic of this
reaction in the current context is the oxidation of Fe(II) to Fe(III) . The reduced
Fe species is olivine, Mgi^FeojySiO^ and the oxidized Fe species is goethite,
with 02(g) as a reactant (Eq. 1.3). This latter species must have been reduced
to water in order that the electrons released by Fe oxidation be absorbed in the
weathering process. Thus the redox aspect is captured by considering how to
balance the postulated weathering reaction:

Mg 163 Feo.37Si0 4 (s) + 2 (g) -> FeOOH(s) + H 2 0(£) (S4.1)

The schematic reaction in Eq. S4.1 can be balanced by first dividing it into
reduction and oxidation half-reactions. The Fe oxidation half-reaction is the
reverse of the reduction half-reaction,

FeOOH(s) + e~ -> M gl 63 Fe .3 7 SiO 4 (s) (S4.2)

which is analogous to Eq. 6.1. Mass balance for Fe is obtained by giving olivine
the stoichiometric coefficient 1/0.37 = 2.7, after which mass balance can be

Oxidation-Reduction Reactions 171

imposed as well on Mg and Si:

FeOOH(s) + 4.4 Mg 2+ + 2.7 Si(OH)^ + e"

^2.7Mg 163 Feo.37Si0 4 (s) (S4.3)

Mass balance for oxygen is achieved by adding two water molecules to the
right side of Eq. S4.3. Proton balance then would require 1 + 2.7(4) — 4 =
7.8 H + to be added to the right side:

FeOOH(s) + 4.4 Mg 2+ + 2.7 Si(OH)^ + e" = 2.7 Mg L63

Feo.3 7 Si0 4 (s) + 2 H 2 0(£) + 7.8 H+ (S4.4)

This reaction can be shown to meet the requirement of overall charge balance.
Note that e _ is essential for this charge balance.

To develop a redox reaction without the aqueous electron, one need only
add to the inverse of Eq. S4.4 the reduction half-reaction for 02(g) in Table 6.1:

2.7 M gl 63 Fe .3 7 SiO 4 (s) + 0.25 2 (g) + 8.8 H+ + 1.5 H 2 0(£)

= FeOOH(s) + 4.4 Mg 2+ + 2.7 Si(OH)° (S4.5)

where 0.5H2O(£) has been canceled from both sides of the result. Equation
S4.5 is a balanced redox reaction showing the weathering of olivine in an oxic
environment to form goethite, aqueous magnesium ions, and silicic acid. The
procedure by which it was developed can be described as follows:

1. Identify the two redox couples participating in the overall redox reaction.

2. For each redox couple, develop a balanced reduction half-reaction in
which 1 mol aqueous electrons is transferred.

3. Combine the two half-reactions developed in Step 2 to cancel the
aqueous electron and produce the required reactant and product redox
species in the overall reaction.

Special Topic 5: The Invention of the pH Meter

While Linus Pauling was beginning his academic career at the California Institute
of Technology, another promising physical chemist came under the tutelage of
Roscoe Gilkey Dickinson, Pauling's mentor as a graduate student (see Special
Topic 2 in Chapter 2). Arnold Beckman had returned to graduate study after a
two-year hiatus provoked by his affection for the woman who was to become his
spouse for more than 60years. What drew Beckman back to Caltech was its strong
commitment to developing new technology as a force for improving the lives of
ordinary people. Like Pauling, he also was asked to join the faculty of his alma
mater upon receiving his Ph.D. degree in 1928. Unlike Pauling, however, Beckman
devoted his research not to the foundations but to the applications of chemical

172 The Chemistry of Soils

science. This focus eventually led him to work on a problem that made him as
well-known as Pauling: the development of a reliable, robust, electrode-based
instrument to measure pH. The story of this invention was summarized nicely
in an article by Elizabeth Wilson commemorating Beckman's 100th birthday.
(Reprinted with permission from Chemical & Engineering News, April 10,
2000, 78(15), p.19. Copyright 2000 American Chemical Society.)

In the 1930s, Arnold Beckman was a chemistry professor at California
Institute of Technology with a reputation for solving practical problems.
Though Beckman prided himself on his considerable and creative teaching
skills, his colleague Robert A. Millikan encouraged his inventive side by sending
him jobs from people who needed technical and scientific help.

Soon, Beckman was augmenting his modest professorial salary with
income from a sideline consulting business, which was particularly welcome
during The Depression.

Among his numerous projects were: methods of testing rock samples for
elusive "colloidal gold" — flecks of the precious metal that eager gold-hunters
believed impregnated otherwise ordinary rock samples; and an inking device
for National Postal Meter that was free of clogging problems that had plagued
previous devices. Beckman even gained a reputation as an expert scientific
witness in court trials.

But the invention that made Beckman a household name was the pH
meter. From a device constructed to help a friend measure the acidity of citrus
juice came a paradigm shift in the way researchers did science.

Beckman's former undergraduate classmate Glen Joseph, a chemist who
worked in the citrus industry in California, desperately needed a consistent,
reliable method of testing citrus juice acidity. Such a measurement was vital to
the industry, because it would help determine if the juice met legal standards
that would allow the fruit to be sold to consumers. If the standards weren't
met, the fruit would then be used to make citric acid or pectin.

To be sure, some methods already existed for testing acidity. Litmus paper,
familiar to anyone who has taken a chemistry lab course, turns red if a sam-
ple's pH is low, and blue if the pH is high. But the sulfur dioxide used by
the citrus industry to preserve the juice bleached litmus paper, rendering it
useless.

There were also electrochemical methods for measuring acidity, as the
current generated from available hydrogen ions in a solution corresponds
to its acidity. These methods were quantitatively precise, but caused Joseph
innumerable headaches.

Hydrogen electrodes, his first choice, were "poisoned" by sulfur dioxide.
Another option was the glass electrode, which was impervious to sulfur diox-
ide. But the electrical current generated by cells with glass electrodes was very
weak, and couldn't be read reliably by the galvanometers Joseph used. He could
increase the current by using very large, thin-walled glass electrodes. Unfor-
tunately, these electrodes were so delicate that they routinely broke, creating
numerous frustrating delays.

Oxidation-Reduction Reactions 173

In desperation, Joseph consulted Beckman. The young inventor almost
immediately came up with a solution that combined the hardiness of a
thick glass electrode with enough electrical sensitivity to produce meaningful
measurement.

The key to Beckman's device was the vacuum tube amplifier. A gal-
vanometer, the measurement instrument of choice, had magnetic needles that
deflected in proportion to the amount of current. But Beckman realized that
by using a vacuum tube-amplifier-based meter instead of a galvanometer, he
would be able to boost the signal to readable levels with a robust but relatively
insensitive glass electrode.

Perhaps Beckman's greatest insight, however, was to put the whole
shebang — electrodes, amplifiers, circuitry — together in one box. This was a
revolutionary concept. Until then, chemists had largely built their instru-
ments from scratch, spending much time assembling and tweaking numerous
components.

This new ready-made, compact device, which Beckman dubbed the
acidimeter, was a time- and sanity-saving godsend. The acidimeter was an
instant hit in Joseph's lab, and it soon became apparent to Beckman that many
others would be clamoring for it — and they did.

Before Beckman's pH meter, "you could measure pH using a platinum or
calomel electrode and a galvanometer and a whole benchful of lab equipment,"
notes Beckman's longtime friend and Beckman Foundation board member
Gerald E. Gallwas. "He made it commercially viable — he put it in a little box
you could carry into an orchard."

Soil Particle Surface Charge

7.1 Surface Complexes

Given the variety of functional groups present in the organic compounds that
form soil humus (sections 3.1 and 3.2), it can be expected that some will come
to reside on the interface between particulate humus and the aqueous phase
in soil. These molecular units protruding from a solid particle surface into
the soil solution are surface functional groups. In the case of soil humus, the
surface functional groups are necessarily organic molecular units, but in gen-
eral they can be bound into either organic or inorganic solids, and they can
have any molecular structure that is possible through chemical interactions.
Because of the variety of possible functional group compositions, a broad
spectrum of surface functional group reactivity is also likely. Superimposed
on this intrinsic variability is that created by the wide range of stereochem-
ical and charge distribution characteristics possible in a heterogeneous solid
matrix. For this reason, no organic surface functional group (e.g., carboxyl)
has single-value quantitative chemical properties (e.g., the proton dissocia-
tion equilibrium constant), but instead can be characterized only by ranges
of values for these properties (Section 3.3). This "smearing out" of chemical
behavior is an important feature that distinguishes surface functional groups
from those bound to small molecules (e.g., oxalic acid).

Figure 5.1 shows a water molecule bearing a positive charge that is bound
to an Al 3+ ion at the periphery of the mineral gibbsite (upper left). This highly
reactive combination of metal cation and water molecule at an interface is
called a Lewis acid site, with the metal cation identified as the Lewis acid. (Lewis

174

Soil Particle Surface Charge 175

acid is the name given to metal cations and protons when their reactions are
considered from the perspective of the electron orbitals in ions. A Lewis acid
initiates a chemical reaction with empty electron orbitals.) Lewis acid sites can
exist on the surface of goethite (Fig. 2.2), if peripheral Fe 3+ ions are bound to
water molecules there, and on the edge surfaces of clay minerals like kaolinite
(Fig. 2.8, left side). These surface functional groups are very reactive because a
positively charged water molecule is quite unstable and, therefore, is exchanged
readily for an organic or inorganic anion in the soil solution, which then can
form a more stable bond with the metal cation. This ligand exchange reaction
is described by Eq. 3.12 for the example of carboxylate and a Lewis acid site.

Lewis acid sites result from the protonation of surface hydroxyl groups,
as indicated in Eq. 3.12a and discussed in sections 2.3 and 2.4 for the miner-
als kaolinite and gibbsite. The protonation reaction, in turn, is provoked by
unsatisfied bond valences with an origin that can be understood in terms of
Pauling Rule 2 (Section 2.1). The surface of goethite, for example, can expose
OH groups that are bound to one, two, or three Fe + (Fig. 2.2). A single Fe — O
bond in goethite has a bond valence of 0.47 vu, according to Eq. 2.3, with the
required data given in Table 2.2 and Problem 2 of Chapter 2. An OH group
bound to a single Fe 3+ evidently would bear a net negative charge and would
require protonation analogously to the same type of OH group in gibbsite or
kaolinite, whereas an OH group bound to two Fe + should be stable, and one
bound to three Fe 3+ can be stabilized by hydrogen bonding to water molecules,
by analogy with what occurs in the bulk goethite structure (Section 2.1). Thus,
the three types of OH group exhibit very different reactivity with respect to
protonation and subsequent ligand exchange.

The plane of oxygen atoms on the cleavage surface of a layer-type alumi-
nosilicate is called a siloxane surface. This plane is characterized by a distorted
hexagonal symmetry among its constituent oxygen atoms (Section 2.3). The
functional group associated with the siloxane surface is the roughly hexagonal
(strictly speaking, ditrigonal) cavity formed by six corner-sharing silica tetra-
hedra, shown on the left in Figure 2.3. This cavity has a diameter of about
0.26 nm and is bordered by six sets of electron orbitals emanating from the
surrounding ring of oxygen atoms.

The reactivity of the siloxane cavity depends on the nature of the electronic
charge distribution in the layer silicate structure. If there are no nearby isomor-
phic cation substitutions to create a negative charge in the underlying layer, the
O atoms bordering the siloxane cavity will function as an electron donor that
can bind neutral molecules through van der Waals interactions (Section 3.4).
These interactions are akin to those underlying the hydrophobic interaction
because the planar structure of the siloxane surface is not particularly compat-
ible with that in bulk liquid water. Therefore, uncharged patches on siloxane
surfaces may be considered hydrophobic regions to a certain degree, with a
relatively strong local attraction for hydrophobic moieties in soil humus or
hydrophobic organic molecules in the soil solution. However, if isomorphic
substitution of Al 3+ by Fe 2+ or Mg 2+ occurs in the octahedral sheet (Table 2.4

176 The Chemistry of Soils

and the right side of Fig. 2.3), a structural charge is created (Eq. 2.8) that can
attract cations and polar molecules (e.g., phenols) or moieties in humus. If
isomorphic substitution of Si 4+ by Al 3+ occurs in the tetrahedral sheet, excess
negative charge is created much nearer to the siloxane surface, and a strong
attraction for cations and polar molecules is generated. Structural charge of
this kind vitiates the otherwise mildly hydrophobic character of the siloxane
surface. Thus 2:1 layer-type clay minerals present a heterogeneous basal sur-
face comprising hydrophobic patches interspersed among charged hydrophilic
sites.

The complexes that form between surface functional groups and con-
stituents of the soil solution are classified analogously to the complexes that
form among aqueous species (Section 4.1). If a surface functional group reacts
with an ion or a molecule dissolved in the soil solution to form a stable
molecular unit, a surface complex is said to exist and the formation reac-
tion is termed surface complexation. Two broad categories of surface complex
are distinguished on structural grounds. If no water molecule is interposed
between the surface functional group and the ion or molecule it binds, the
complex is inner-sphere. If at least one water molecule is interposed between
the functional group and the bound ion or molecule, the complex is outer-
sphere. As a general rule, outer-sphere surface complexes involve electrostatic
bonding mechanisms and, therefore, are less stable than inner-sphere surface
complexes, which necessarily involve either ionic or covalent bonding, or some
combination of the two. These concepts are quite parallel with those developed
in Section 4.1 for aqueous species and in Section 3.5 for bridging complexes.
Seen in this light, Figure 3.5 shows Ca 2+ in an inner-sphere surface complex
with a charged site on a siloxane surface while at the same time forming an
outer-sphere complex with carboxylate. Figure 3.6 shows the reverse arrange-
ment of the complexes: inner-sphere with carboxylate and outer-sphere with
a charged site on the siloxane surface. Bridging complexes thus may also be
considered as ternary surface complexes involving an organic ligand, a metal
cation, and a charged surface site.

Figure 7.1 illustrates the structure of the outer-sphere surface complex
formed between Na + and a surface site on the siloxane surface of montmoril-
lonite. At about 50% relative humidity, a stable hydrate forms in which there
are two layers of water molecules. The Na + tends to adsorb as solvated species
on the siloxane surface near negative charge sites originating in the octahedral
sheet from isomorphous substitution of a bivalent cation for Al 3+ . This outer-
sphere complex occurs as a result of both the strong solvating characteristics
of Na + and the physical impediment to direct contact between Na + and the
site of negative charge posed by the layer structure itself. The way in which this
negative charge is distributed on the siloxane surface is not well-known, but
if the charge tends to be delocalized ("smeared out" over several oxygen ions),
that would lend itself to outer-sphere surface complexation. It is pertinent to
note that the molecular structure of the solvation complex in Figure 7.1 is very
similar to that observed for solvated Na + in concentrated aqueous solutions.

Soil Particle Surface Charge 177

Figure 7.1. An outer-sphere surface complex formed between Na+ and a charged
surface site on montmorillonite. Visualization courtesy of Dr. Sung-Ho Park.

Figure 7.2 illustrates an outer-sphere surface complex formed between
Pb + and a hydrated surface site on the Al oxide, corundum (Section 2.1).
The exposed surface comprises triangular rings of six oxygen ions in Al0 6 ~
octahedra, with each O 2- bonded to a pair of neighboring Al 3+ . Like the
basal planes in gibbsite, this surface is protonated when in contact with an
aqueous solution. The outer-sphere surface complex has Pb + coordinated to
three water molecules that are also hydrogen bonded to surface hydroxyls on
the border of an octahedral cavity in the center of one of the triangular rings
of protonated oxygen ions. Two other water molecules solvate the adsorbed
Pb + to give a total solvation shell coordination number of 5, similar to what
is observed for Pb 2+ in concentrated aqueous solutions.

Inner-sphere surface complexes between K + or Cs + and the siloxane sur-
face of a 2:1 clay mineral with extensive Al + substitutions in the tetrahedral
sheets are especially stable. This type of surface complex requires coordina-
tion of the monovalent cation with 12 oxygen atoms bordering two opposing
siloxane cavities. The layer charge in the clay mineral vermiculite is large
enough (Table 2.4) that each siloxane cavity in a basal plane of the min-
eral can complex one monovalent cation. Moreover, the ionic radius of K +
(Table 2.1) is essentially equal to that of a cavity. This combination of charge
distribution and stereochemical factors gives K-vermiculite surface complexes
great stability and is the molecular basis for the term potassium fixation,
colloquial

As mentioned earlier, the hydroxyl group coordinated to one Fe 3+ in
goethite can be protonated to form a Lewis acid site. The water molecule can
then be exchanged as inEq. 3.12 to allow formation of an inner-sphere surface
complex with the oxyanion HP0 4 - . This surface complex is illustrated in
Figure 7.3. It consists of an HP0 4 - bound through its oxygen ions to a pair of

178 The Chemistry of Soils

Surface H

Surface Oxygen

Figure 7.2. An outer-sphere surface complex formed between Pb2+ and the hydrox-
ylated surface of a— AI2O3 (corundum). After Bargar, J., S.N. Towle, G.E. Brown, and
G.A. Parks (1997) XAFS and bond-valence determination of the structures and com-
positions of surface functional groups and Pb(II) and Co(II) sorption products on
single-crystal a-Al 2 3 . /. Colloid Interface Sci. 185: 473-492.

Figure 7.3. An inner-sphere surface complex formed between a biphosphate anion
(HP0 4 ) and two adjacent Fe + in goethite. Visualization courtesy of Dr. Kideok
Kwon.

Soil Particle Surface Charge 179

adjacent Fe + cations (binuclear surface complex). The configuration of the o-
phosphate unit is compatible with the grooved structure of the goethite surface,
thus providing stereochemical enhancement of the stability of the inner-sphere
complex. Inner-sphere complexes can also form through the ligand exchange
of other oxyanions (e.g., selenite, arsenate, borate) with protonated OH groups
on goethite and other metal oxyhydroxides.

7.2 Adsorption

Adsorption is the process through which a chemical substance reacts at the
common boundary of two contiguous phases. If the reaction produces enrich-
ment of the substance in an interfacial layer, the process is termed positive
adsorption. If, instead, a depletion of the substance is produced, the process is
termed negative adsorption. If one of the contiguous phases involved is solid
and the other is fluid, the solid phase is termed the adsorbent and the matter
that accumulates at its surface is an adsorbate. A chemical species in the fluid
phase that potentially can be adsorbed is termed an adsorptive. As indicated
in Section 7.1, if an adsorbate is immobilized on the adsorbent surface over
a timescale that is long, say, when compared with that for diffusive motions
of the adsorptive, then the adsorbate and the site on the adsorbent surface to
which it is bound are termed a surface complex.

Adsorption experiments involving solid particles typically are performed
in a sequence of three steps: (1) reaction of an adsorptive with an adsorbent
contacting a fluid phase of known composition under controlled tempera-
ture and applied pressure for a prescribed period of time, (2) separation of the
adsorbent from the fluid phase after reaction, and (3 ) quantitation of the chem-
ical substance undergoing adsorption, both in the supernatant fluid phase and
in the separated adsorbent slurry that includes any entrained fluid phase. The
reaction step can be performed in either a closed system (batch reactor) or an
open system (flow-through reactor), and can proceed over a time period that
is either quite short (adsorption kinetics) or very long (adsorption equilibra-
tion) compared with the natural timescale for achieving a steady composition
in the reacting fluid phase. The separation step is similarly open to choice, with
centrifugation, filtration, or gravitational settling being convenient methods
to achieve it. The quantitation step, in principle, should be designed not only
to determine the moles of adsorbate and unreacted adsorptive, but also to
verify whether unwanted side reactions, such as precipitation of the adsorp-
tive or dissolution of the adsorbent, have unduly influenced the adsorption
experiment.

Ion adsorption on soil particle surfaces can take place via the three mech-
anisms illustrated in Figure 7.4 for a monovalent cation on the siloxane surface
of a 2:1 clay mineral like montmorillonite. The inner-sphere surface complex
shown involves the siloxane cavity, as described in Section 7.1, whereas the
outer-sphere surface complex shown includes the cation solvation shell and

180 The Chemistry of Soils

Modes of Cation Adsorption
by 2:1 Layer Type Clay
Minerals

Diffuse Ion

Interlayer
Complex

Outer-Sphere
Complexes

External Basal
Plane Complexes

Figure 7.4. The three modes of ion adsorption, illustrated for cations adsorbing on
montmorillonite.

is similar to that depicted in Figure 7.2. These two localized surface species
constitute the Stern layer on an adsorbent. If a solvated ion does not form a
complex with a charged surface functional group, but instead screens a surface
charge in a delocalized sense, it is said to be adsorbed in the diffuse-ion swarm,
also shown in Figure 7.4. This last adsorption mechanism involves ions that are
fully dissociated from surface functional groups and are, accordingly, free to
hover nearby in the soil solution. The diffuse-ion swarm and the outer-sphere
surface complex mechanisms of adsorption involve almost exclusively electro-
static bonding, whereas inner-sphere complex mechanisms are likely to involve
ionic as well as covalent bonding. Because covalent bonding depends signifi-
cantly on the particular electron configurations of both the surface group and
the complexed ion, it is appropriate to consider inner-sphere surface complex-
ation as the molecular basis of the term specific adsorption. Correspondingly,
diffuse-ion screening and outer-sphere surface complexation are the molec-
ular basis for the term nonspecific adsorption. Nonspecific refers to the weak
dependence on the detailed electron configurations of the surface functional
group and adsorbed ion that is to be expected for the interactions of solvated
species.

Readily exchangeable ions in soil are those that can be replaced easily
by leaching with an electrolyte solution of prescribed composition, concen-
tration, and pH value. Despite the empirical nature of this concept, there
is a consensus that ions adsorbed specifically (like HP0 4 - in Fig. 7.3) are
not readily exchangeable. Thus, experimental methods to determine readily
exchangeable adsorbed ions must avoid extracting specifically adsorbed ions.
From this point of view, fully solvated ions adsorbed on soils are readily exchange-
able ions, with the molecular definition of readily exchangeable thus based on
the diffuse-ion swarm and outer-sphere complex mechanisms of adsorption.

More generally, the interactions between adsorptive ions and soil
particles can be portrayed as a web of sorption reactions mediated by two

Soil Particle Surface Charge 181

parameters: timescale and adsorbate surface coverage. Surface complexes are
the products of these reactions when timescales are sufficiently short and
surface coverage is sufficiently low, with "sufficiently" always being defined
operationally in terms of conditions attendant to the sorption process. As
timescales are lengthened (e.g., longer than hours) and surface coverage
increases, or as chemical conditions are altered (e.g., pH changes) for a fixed
reaction time, adsorbate "islands" comprising a small number of ions bound
closely together may form. These reaction products are termed multinuclear
surface complexes by analogy with their counterpart in aqueous solution chem-
istry. They are the more likely for adsorptive ions that readily form polymeric
structures in aqueous solution. Multinuclear surface complexes may in turn
grow with time to become colloidal structures that are precursors of either
surface polymers or, if they are well organized on a three-dimensional lattice,
surface precipitates. Thus, sorption processes need not exhibit the inherently
two-dimensional character of positive adsorption processes, although both
involve the accumulation of a substance at an interface.

7.3 Surface Charge

Solid particle surfaces in soils develop an electrical charge in two principal
ways: either from isomorphic substitutions in soil minerals among ions of
differing valence, or from the reactions of surface functional groups with ions
in the soil solution. The electrical charge developed by these two mechanisms
is expressed conventionally in moles of charge per kilogram (mol c kg , see
the Appendix). Four different types of surface charge contribute to the net total
particle charge in soils, denoted a p . Each of these components can be positive,
zero, or negative, depending on soil chemical conditions.

Two components of cf p have been described in previous chapters. Struc-
tural charge, ao, defined in Eq. 2.7, arises from isomorphic substitutions in 2:1
clay minerals (Section 2.3) and from cation vacancy defects and in manganese
oxides (Section 2.4). Although ao can be calculated with chemical composition
data for a mineral specimen, in a soil sample it is measured conventionally as
Cs-accessible surface charge following a reaction of the sample with 50 mol m -3
CsCl at pH 5.5 to 6.0. Briefly, the soil is saturated with Cs by repeated wash-
ing in CsCl, with a final supernatant solution ionic strength of 50 mol m.
After centrifugation, the supernatant solution is discarded and the remaining
entrained CsCl solution is removed by washing with ethanol. The samples are
then dried at 65 °C for 48 hours to enhance formation of inner-sphere Cs sur-
face complexes. Next, the samples are washed in 10 molm -3 LiCl solution to
eliminate outer-sphere surface complexes of Cs. The suspension is centrifuged,
and the supernatant LiCl solution is removed for analysis, leaving only a slurry
containing the soil sample and entrained LiCl solution. Finally, Cs is extracted
with 1 mol dm -3 ammonium acetate (NH4OAC) solution, and the LiCl and
NH4OAC solutions are analyzed for Cs. Permanent structural charge is then

182 The Chemistry of Soils

calculated as minus the difference between moles Cs in the NH4OAC extract
and moles Cs in the entrained LiCl solution, per kilogram of dry soil. This
method is reliable even for highly heterogeneous samples that comprise both
crystalline and amorphous minerals, organic matter, and biota. Its sensitivity
is such that |o"o| values < 1 mmol c kg are detectable.

The net proton charge, oh, discussed at length in Section 3.3 as an attribute
of soil humus, is defined for unit mass of any charged particle as the difference
between the moles of protons and the moles of hydroxide ions complexed
by surface functional groups (cf. Eq. 3.5). Thus, protons and hydroxide ions
adsorbed in the diffuse-ion swarm are not included in the definition of an-
As noted in Section 3.3, the measurement of cth remains as an experimental
challenge, but consensus exists that it makes a very important contribution to
CTp over a broad range of pH. It receives contributions from all acidic surface
functional groups in a soil, including those exposed on humus, on the edges of
clay mineral crystallites, and on oxyhydroxide minerals. The sum of structural
and net adsorbed proton charge defines the intrinsic charge, o"; n ,

Om^cro + aH (7.1)

which is intended to represent components of surface charge that develop
solely from the adsorbent structure.

The net adsorbed ion charge is defined formally by the equation

Aq = ais + aos + o" d (7.2)

which refers, specifically, to the net charge of ions adsorbed in inner-sphere
surface complexes (IS), in outer-sphere surface complexes (OS), or in the
diffuse-ion swarm (d). The utility of Eq. 7.2 depends on the extent to which
experimental detection and quantitation of these surface species is possible.
The partitioning of surface complexes into inner-sphere and outer-sphere is
not always possible (or required), however, and Eq. 7.2 can alternatively be
written in the simpler form

Aq=a s + CTd (7.3)

where as denotes the Stern layer charge (cf. Fig. 7.4) representing all adsorbed
ions not in the diffuse-ion swarm. This latter conceptual distinction, based
largely on adsorbed ion mobility, is epitomized by defining the net total particle
charge, cr p :

o p = a in + a s (7.4)

which is the surface charge contributed by the adsorbent structure and by
adsorbed ions that are immobilized into surface complexes (i.e., adsorbed
ions that do not engage in translational motions that may be likened to the
diffusive motions of a free ion in aqueous solution). The adsorbed ions that

Soil Particle Surface Charge 183

do engage in more or less free diffusive motions must nonetheless contribute
a net charge that balances the net total particle charge:

Op + a d = (7.5)

Equation 7.5 is the condition of surface charge balance for soil particles. It states
simply that any electrical charge these particles may bear is always balanced by
a counterion charge in the diffuse swarm of electrolyte ions near their surfaces.
An alternative form of Eq. 7.5 can be written down at once after combining
Eq. 7.1 with eqs. 7.3. to 7.5:

ffo + cr H + Aq = (7.6)

Equation 7.6, which does not require molecular-scale concepts, mandates the
overall electroneutrality of any soil sample that has been equilibrated with an
aqueous electrolyte solution. Structural charge and the portion of net particle
charge attributable to surface-complexed protons or hydroxide ions must be
balanced with the net surface charge that is contributed by all other adsorbed
ions and by H + or OH - in the diffuse-ion swarm.

Equation 7.6 can be used to test experimental surface charge data for self-
consistency. A convenient approach is to plot Aq against an over a range of pH
values for which these two surface charge components have been measured.
A simple rearrangement of Eq. 7.6,

Aq = -oh - o-o (7.7)

shows that the slope of this Chorover plot must be equal to — 1, with both
its y- and x- intercepts equal to - oq. Figure 7.5 illustrates the application of
Eq. 7.7 to an Oxisol, comprising kaolinite, metal oxides, and quartz intermixed
with humus, that was equilibrated with LiCl solution at three different ionic
strengths over the pH range 2 to 6. The line through the data is based on a
linear regression equation,

Aq = -1.01 ± 0.07cr H + 12.5 ± 0.8 (R 2 = 0.92)

with both Aq and oh expressed in units of millimoles of charge per kilogram
and with 95% confidence intervals following the values of the slope and inter-
cept. The value of cro measured independently by the Cs + method is -12.5
± 0.04 mmol c kg -1 , which is in excellent agreement with both the y- and
x-intercepts.

7.4 Points of Zero Charge

Points of zero charge are pH values at which one of the surface charge com-
ponents in Eqs. 7.5 and 7.6 becomes equal to zero under given conditions of
temperature, applied pressure, and soil solution composition. Three standard
definitions are given in Table 7.1.

184 The Chemistry of Soils

~i — ' — i — ■ — i — ■ — i — ■ — i — ■ — i — > — r
-25-20-15-10-5 5 10 15 20 25

<t h (mmol c kg" 1 )

Figure 7.5. A Chorover plot for a cultivated kaolinitic Oxisol suspended in Li CI solu-
tions of varying concentration (open circles = 1 mM, crosses = 5 mM, and filled circles
= 10 mM) and pH 2 to 6. The vertical and horizontal dashed lines are the coordinate
axes. Their intersections with the linear plot are required to be equal if charge balance
is confirmed. Original graph courtesy of Dr. Jon Chorover.

The p.z.n.p.c. is the pH value at which the net adsorbed proton charge
is equal to zero. A straightforward method to determine this pH value is
to measure Aq as a function of pH and then locate the pH value at which
Aq = -o"o> thus taking direct advantage of Eq. 7.6 (Fig. 7.6), given that a separate
measurement of o"o has been made. Most published reports of p.z.n.p.c. values
based on the use of titration measurements to determine o"h resort to the
device of choosing o"h = at the crossover point of two <5aH,titr versus pH
curves that have been determined at different ionic strengths. Unfortunately,
as mentioned in Section 3.3, each such curve is, in principle, offset differently
from a true o"h curve by an unknown San.titr that corresponds to the particular
initial state of the titrated system, thus making the crossover point illusory.

Equation 7.6 imposes a constraint on changes in the net adsorbed proton
charge and/or net adsorbed ion charge that may occur in response to controlled

Table 7.1

Some points of zero charge.

Symbol Name Definition

p.z.n.p.c. Point of zero net proton charge 0"h =

p.z.n.c. Point of zero net charge Aq =

p.z.c. Point of zero charge a p =

Soil Particle Surface Charge 185

V 25

Manaus clay
LiCI background
25°C

loj

$£' °f^^ P-Z-n-P-C

V,fo/0| |

: , -Ao , + 36 i \ 1 1

2 f 6 3

4
-log [H + ]

Figure 7.6. Plots of net adsorbed ion charge against pH for an uncultivated kaolinitic
Oxisol suspended in Li CI solutions with the same varying concentration and pH values
as in Figure 7.5. The upper horizontal line intersects each graph at the p.z.n. p. c, whereas
the lower horizontal line intersects each graph at the p.z.n.c. Data from Chorover, J., and
G. Sposito (1995) Surface charge characteristics of kaolinitic tropical soils. Geochim.
Cosmochim. Acta 59:875-884.

changes in adsorbate or adsorptive composition at fixed temperature (T) and
applied pressure (P):

8a H + SAq =

(7.8)

where 8 represents an infinitesimal shift caused by any mechanism that does
not alter Oq. For example, if the ionic strength (I) of the aqueous solution
equilibrated with a soil is changed at fixed T and P, Eq. 7.8 can be expressed as

V 9I /T,P V 9I /T,P

(7.9)

This constraint may be applied to the definition of the point of zero salt effect
(p.z.s.e.),

(pH = p.z.s.e.)

(7.10)

T,P

186 The Chemistry of Soils

to show that the crossover point of two an versus pH curves must also be that
of two Aq versus pH curves. This can be used to verify the accuracy of p.z.s.e.
values inferred from the crossover point of 5aH,titr curves.

The p.z.n.c. is the pH value at which the net adsorbed ion charge is equal
to zero. A common laboratory method is to utilize index ions, such as Li + and
Cl _ , in the determination of p.z.n.c. from a Aq versus pH curve (Fig. 7.6).
Evidently, the value of p.z.n.c. will depend on the choice of index ions, although
this dependence tends to be small if the ions are chosen from the following
group: Li + , Na + , K + , Cl~, ClO^~, and NO^~. As a broad rule, p.z.n.c. values
for silica, humus, clay minerals, and most manganese oxides are less than
pH 4, whereas those for aluminum and iron oxyhydroxides and for calcite are
more than pH 7. Thus, p.z.n.c. tends to increase as chemical weathering of a soil
proceeds if there is an attendant loss of humus and silica (cf. Table 1.7).

The p.z.c. is the pH value at which the net total particle charge is equal to
zero. Thus, by Eq. 7.5, at the p.z.c, there is no surface charge to be neutralized
by ions in the diffuse swarm. Therefore, the p.z.c. could be measured by ascer-
taining the pH value at which a perfect charge balance exists among the ions
in an aqueous solution with which soil particles have been equilibrated. More
commonly, p.z.c. is inferred from the pH value at which a suspension of par-
ticles flocculates rapidly — a condition that is produced by the dominance of
attractive van der Waals interactions (Section 3.4) over the coulomb repulsion
between particles that is created by a nonzero net total particle charge.

The charge balance conditions in eqs. 7.5 and 7.6 lead to three broad
statements about points of zero charge known as PZC Theorems. The first of
these theorems concerns the relationship between p.z.n.p.c. and p.z.n.c. At the
latter point of zero charge, Eq. 7.5 reduces to the condition

a + a H = (pH = p.z.n.c). (7.11)

If p.z.n.c. > p.z.n.p.c, an must have a negative sign in Eq. 7.11 because an
always decreases as pH increases, and cfh = at p.z.n.p.c. It follows that the
structural charge ao > if p.z.n.c. > p.z.n.p.c. Similarly, if p.z.n.c. < p.z.n.p.c,
ao < 0. Therefore, we have the first PZC Theorem:

1. The sign of the difference (p.z.n.c. -p.z.n.p.c.) is the sign of the structural
charge.

For example, p.z.n.c. < p.z.n.p.c. typically for kaolinitic Oxisols (Fig. 7.6)
and for specimen kaolinite samples, indicating at once that a negative struc-
tural charge exists in these materials, likely from the presence of 2:1 layer-type
clay minerals, given the typical lack of isomorphic substitutions in kaolinite.
More generally, soil particles with a surface chemistry dominated by 2:1 clay
minerals or manganese oxides (ao < 0) must always have p.z.n.c. values below
their p.z.n.p.c. values.

A corollary of PZC Theorem 1 is that, for soilparticles without 2:1 clay min-
erals (and, strictly speaking, without oxide minerals having structural charge)
p.z.n.c. = p.z.n.p.c. Equality of the two points of zero charge means that the pH

Soil Particle Surface Charge 187

value at which an is equal to zero can be determined through ion adsorption
measurements alone.

The difference between p.z.n.c. and p.z.c. is that a charged diffuse-ion
swarm exists at the former pH value, whereas it cannot exist at the latter
pH value. The use of suspension flocculation to signal p.z.c. is compromised
by the fact that flocculation usually occurs in the presence of a small — but
nonzero — electrostatic repulsive force that is not strong enough to preclude
van der Waals attraction from inducing flocculation. However, surface charge
balance, as expressed by combining eqs. 7.4 and 7.5,

Oin + as + a d = (7.12)

yields a relationship between p.z.n.c. and p.z.c. Suppose that the Stern layer
charge as = at the p.z.n.c. Then aj must also vanish because of Eq. 7.12 and
the fact that cfj n = at the p.z.n.c. But a<j = means pH = p.z.c. Therefore,
p.z.c. = p.z.n.c. if as = at the p.z.n.c. Conversely, if p.z.c. = p.z.n.c, then
a; n = = ad and, again by Eq. 7.12, as = of necessity. The general
conclusion to be drawn is in the second PZC theorem:

2. The p.z.c. is equal to the p.z.n.c. if and only if the Stern layer charge is zero
at the p.z.n.c.

Note that PZC Theorem 2 is trivially true if the only adsorbed species are
those in the diffuse-ion swarm. If surface complexes exist, PZC Theorem 2
will not hold unless the ions adsorbed in them (other than H + or OH - ) meet
a condition of zero net charge at the p.z.n.c. This might occur for monovalent
ions adsorbed "indifferently" in outer-sphere surface complexes by largely
electrostatic interactions (e.g., Li + and Cl _ ). Electrolytes for which as = at
the p.z.n.c. are indeed termed indifferent electrolytes, in the sense that relatively
weak electrostatic interactions cause their more or less equal adsorption. The
p.z.c. values of particles suspended in solutions of indifferent electrolytes thus
can be determined by ion adsorption measurements.

As originally conceived, the Stern layer comprises both inner-sphere and
outer-sphere surface complexes (Fig. 7.4). If these species do not combine to
yield zero net charge at the p.z.n.c, then p.z.c. ^ p.z.n.c, according to PZC
Theorem 2. The close relationship between p.z.c. and as can be exposed further
by applying the charge balance constraint in Eq. 7.8 at the p.z.c:

Sa u + 8o s = (pH = p.z.c.) (7.13)

which thus refers to changes under which a p remains equal to zero. If the Stern
layer charge is made to increase, say, by increasing the amount of surface-
complexed cations, then, according to Eq. 7.13, the net proton charge must
compensate this change by decreasing, which in turn requires the p.z.c. to
increase. The pH value at which an + as balances oq must be higher, as as
becomes higher, in order that an will be negative enough to meet the condition
of charge balance. In the same way, the pH value at which a d = must be
lower, as as becomes lower through anion adsorption, in order that oh will

188 The Chemistry of Soils

become positive enough to compensate exactly the decrease in as. This line of
reasoning is epitomized in the third PZC theorem:

3. If the Stern layer charge increases, thep.z.c. also increases, and vice versa.

Theorem 3 indicates the role of cation surface complexation in increasing
p.z.c. and that of anion surface complexation in decreasing p.z.c. It does not
imply, however, that shifts in p.z.c. signal the effect of strong ion adsorption
(specif c adsorption), because changes in the number of outer-sphere surface
complexes in the Stern layer are sufficient to change p.z.c.

7.5 Schindler Diagrams

Additional insight into the differences between readily exchangeable and
specifically adsorbed ions can be obtained through the use of Schindler
diagrams. A Schindler diagram is a banded rectangle in which the charge
properties of an adsorbent and an adsorptive are compared as a function of
pH in the range normally observed for soil particles, say, pH 3 to 9.5. The top
band contains a vertical line denoting the p.z.n.c. of the adsorbent. The central
band contains vertical lines denoting either the value of —log *K for hydrolysis
(based on water as a reactant) of metal cation adsorptives, or the value of log
K for protonation (based on the proton as a reactant) of ligand adsorptives:

m + (m n+ + * (MOH (m " 1)+ )(H + )

M m+ + H 2 0(£) = MOH (m_1)+ + H+ *K = -—

(M m +)

(7.14a)

I/" + H+ = ffl^- 1 )- K = (HL(< " 1) " ) (7.14b)

(I/-)(H+)

The bottom band shows a horizontal line depicting the range of pH over which
adsorption is to be expected when based solely on unlike charge attraction
between the adsorbent and the adsorptive. This pH range, therefore, indicates
conditions under which the adsorbent can surely function as a cation or anion
exchanger. If adsorption is observed to occur at pH values outside this range,
specific adsorption mechanisms are implied.

As a first example of a Schindler diagram, consider an adsorbent com-
posed primarily of clay minerals and humus, with the adsorptive being an ion
of an indifferent electrolyte (e.g., Li + , Na + , Cl _ , or NO^~). The p.z.n.c. of the
adsorbent will not likely exceed 4.0, and the -log *K value for metal hydrolysis
as well as log K for anion protonation of indifferent electrolyte adsorptives
always will lie outside the pH range between 3 and 9. Therefore, the Schindler
diagram will feature a top band with a vertical line at pH 4 (or possibly to its
left), a central band that has no vertical lines, and a bottom band with either a
horizontal line extending to the right of pH 4 (cations) or one extending to the
left of pH 4 (anions). It follows that adsorbents comprising principally humus
and clay minerals (e.g., soils from temperate grassland regions) will function

Soil Particle Surface Charge 189

3 4 5 6 7 8 9
PH

Figure 7.7. Schindler diagram for cations adsorbing on a soil with a clay fraction that
is dominated by humus and clay minerals.

Pb 2 ^

~ 2+
Cu

3 4

5 6 7
pH

3 9

Figure 7.8. Schindler diagram for metal cations adsorbing on Fe(OH)3, a common
product of Fe(III) precipitation in soils undergoing alternate flooding and drying
conditions.

effectively as cation exchangers under most soil conditions. Conversely, adsor-
bents comprising principally iron and aluminum oxides (e.g., uncultivated
subsoils from the humid tropics), for which p.z.n.c. > 7 typically, will func-
tion effectively as anion exchangers. These trends are illustrated for adsorptive
cations in Figure 7.7.

A second example can be developed for the adsorbent Fe(OH)3 and the
adsorptives Pb , Cu , and Cd . The relevant p.z.n.c. value is 7.9, and
the respective -log *K values are 7.7, 8.1, and 10.1. Therefore, the Schindler
diagram for this system features a top band with a vertical line at pH 7.9, a
central band with vertical lines at pH 7.7 and 8.1, and a bottom band with
a horizontal line from pH 7.9 to 9.5 (Fig. 7.8). The rather narrow range of
pH over which the adsorbent can function as a cation exchanger is apparent.
The adsorption reactions of Pb 2+ and Cu 2+ with Fe(OH)3 are in fact typically
observed to be very strong at pH < p.z.n.c. while the adsorbent surface is still
positively charged, implying a specific adsorption mechanism. The adsorption
of Cd 2+ , on the other hand, often only commences on Fe(OH)3 for pH >
p.z.n.c. and, therefore, is consistent with a cation exchange mechanism.

The same approach can be used to analyze a calcareous soil reacting with
borate in solution. The relevant p.z.n.c. value is 9.5, and log K for B(OH)^~
is 9.23. Therefore, the corresponding Schindler diagram has a top band with

190 The Chemistry of Soils

B(OH):

B(OH),

3 4 5 6 7 8 9
PH

Figure 7.9. Schindler diagram for borate adsorbing on a calcareous Entisol.

a uniformly positive adsorbent surface charge indicated, a central band with
a vertical line at pH 9.2, and a bottom band with a horizontal line extending
over the very narrow range of pH between 9.2 and 9.5 (Fig. 7.9). Quite clearly,
then, specific adsorption mechanisms are involved if the reaction of borate
with this soil is significant at pH < 9.2. At pH values less than 9.2, borate
anions do exist to some degree and can be attracted to the positively charged
adsorbent in increasing numbers as pH increases from 7 to 9. At pH values
more than 9.2, the adsorptive is predominantly anionic, but now the adsorbent
is also becoming increasingly negatively charged, leading to an expected sharp
fall-off in adsorption at pH > p.z.n.c.

For Further Reading

Chorover, J., M. K. Amistadi, and O. A. Chadwick. (2004) Surface charge
evolution of mineral-organic complexes during pedogenesis in Hawai-
ian basalt. Geochim. Cosmochim. Acta 68:4859-4876. This article offers a
comprehensive application of surface charge concepts and definitions to
soils in a chronosequence for which a variety of chemical, mineralogical,
and spectroscopic properties are known.

Johnston, C. T., and E. Tombacz. (2002) Surface chemistry of soil minerals,
pp. 37-67. In: J. B. Dixon and D. G. Schulze (eds.), Soil mineralogy with
environmental applications. Soil Science Society of America, Madison, WI.
An excellent survey of surface charge concepts applied to soil minerals
and humus that can be read with profit as a companion to the current
chapter.

Sposito, G. (1998). On points of zero charge. Environ. Sci. Technol. 32:2815-
2819, Sposito, G. (1999). Erratum: On points of zero charge. Environ. Sci.
Technol. 33:208. An in-depth treatment of the PZC Theorems together
with some of the conceptual issues arising in the measurement of points
of zero charge.

Yu, T R. (1997) Chemistry of variable charge soils. Oxford University Press,
New York. This research monograph provides a detailed survey of the

Soil Particle Surface Charge 191

chemical properties of soils with surface charge characteristics that are
highly pH dependent.
Zelazny, L. W., L. He, and A. Vanwormhoudt. (1996) Charge analysis of soils
and anion exchange, pp. 1231—1253. In: D. L. Sparks (ed.), Methods of
soil analysis: Part 3. Chemical methods. Soil Science Society of America,
Madison, WI. This book chapter presents a useful discussion of laboratory
methods for measuring surface charge components and points of zero
charge.

Problems

The more difficult problems are indicated by an asterisk.

1. The table presented here shows the pH dependence of the amounts of Na +
and Cl _ absorbed by a kaolinitic Brazilian Oxisol at two inoic strengths.
Calculate Aq = n^a—n^i as a function of pH, estimating its precision, and
determine the p.z.n.c. of the soil at both ionic strengths, also estimating
its precision

1 = 9 mol m

-3

1 = 30 mol

m- 3

r>Na

nci

nNa

n C l

(mmol kg~ 1 )

2.55

1.02 ±0.12

6.39 ±0.41

2.57

1.51 ±0.52

9.79 ± 0.94

2.76

1.21 ±0.20

5.73 ±0.52

2.79

2.03 ±0.21

8.28 ±0.62

2.87

1.30 ±0.47

5.57 ±0.36

2.92

1.71 ±0.68

7.64 ± 0.54

3.04

1.51 ±0.40

4.71 ±0.41

3.09

2.37 ±0.16

7.77 ±0.56

3.46

1.78 ±0.16

3.88 ±0.58

3.30

2.54 ±0.30

6.37 ±0.70

3.63

2.11 ±0.28

3.78 ±0.33

3.57

3.51 ±0.45

5.72 ± 0.40

3.90

2.05 ±0.10

2.51 ±0.91

4.04

4.30 ±0.67

4.62 ±0.13

4.16

2.01 ±0.23

2.60 ± 0.44

4.35

5.27 ±0.85

3.75 ± 0.65

4.41

3.60 ±0.33

1.34 ±0.52

4.63

7.13 ±0.91

2.46 ± 0.62

4.95

4.49 ± 0.46

1.14 ±0.45

4.84

8.71 ±0.75

1.86 ±0.70

[Hint: If a» a and oq are the respective standard deviations of n^ a and

n a , then a Aq = (cr^a + cTq) /2 -]

2. The amount of Cs + adsorbed by gibbsite particles suspended in CsCl
solution was found to increase linearly from essentially to 20 mmol
kg as pH increased from 7.7 to 9.0, whereas the amount of Cl adsorbed
decreased linearly from 13 mmolkg -1 to essentially mmolkg -1 as pH
increased from 4 to 9. Calculate p.z.n.p.c. for this mineral.

192 The Chemistry of Soils

3. The table presented here shows the pH dependence of an for the kaolinitic
Oxisol described in Problem 1. Determine p.z.n.p.c. taking into account
the precision of the data.

1 =

= 30 mol m 3

= 9 mol m 3

an (mmol c kg~ 1 )

oh (mmol c kg~ 1 )

2.57

58.11 ± 1.15

2.55

50.63 ± 6.62

2.79

41.73 ±2.78

2.76

37.36 ±3.59

2.92

34.08 ± 1.72

2.87

29.74 ±6.31

3.09

25.99 ± 1.78

3.04

23.03 ±2.05

3.30

18.49 ± 2.69

3.46

9.64 ± 1.42

3.57

11.55 ± 1.41

3.63

6.67 ±0.99

4.04

1.21 ± 1.68

3.90

3.74 ± 1.71

4.35

-4.06 ± 1.66

4.16

0.09 ± 1.62

4.63

-7.52± 1.01

4.41

-1.81 ±0.66

4.84

-10.88 ±2.10

4.95

-4.94 ± 1.04

4. Compare p.z.n.c. and p.z.n.p.c. at each ionic strength for the Oxisol
described in Problems 1 and 3. What can be deduced about the existence
of structural charge in this soil?

"5. The table presented here shows the pH dependence of Aq and 5(XH,titr at
two ionic strengths for a California Alfisol suspended in NaCl solution.
For this soil, the Cs + method yields oq = —64.5 ± 0.2 mmol c kg -1 .

Kmol L- 1 ;

) pH

Aq (mmol c

kg- 1 )

5cr H ,titr (mmolc kg 1 )

0.05

4.20 ±0.01

63 ± 12

48.1 ±0.3

4.59 ±0.02

72 ±

35.4 ±0.2

5.53 ± 0.04

94 ±

16.20 ±0.04

5.84 ± 0.04

91 ±

12.40 ±0.05

6.52 ±0.07

102 ±

2.50 ±0.01

7.04 ± 0.04

104 ±

0.03 ±0.01

7.30 ±0.08

117 ±

-0.08 ±0.01

7.84 ± 0.08

115 ±

-1.60 ±0.08

0.02

4.30 ±0.04

81 ±

56.1 ±0.6

4.76 ±0.03

92 ±

37.4 ±0.2

5.35 ±0.02

103 ±

25.0 ±0.1

5.82 ±0.02

108 ±

17.02 ±0.06

6.51 ±0.01

124 ±

7.50 ±0.01

7.08 ±0.07

116 ±

0.24 ±0.01

7.56 ± 0.09

122 ±

-0.17 ±0.01

7.91 ±0.09

128 ±

-0.97 ±0.01

Soil Particle Surface Charge 193

a. Calculate cth as a function of pH for each ionic strength, including an
estimate of its precision.

b. Plot your results on a single graph with error bars on each data point
indicating the imprecision in both oh and pH. (Hint: The standard
deviation of a sum or difference of two quantities is estimated as the
square root of the sum of the squares of the standard deviations for
the two quantities.)

6. Estimate p.z.n.p.c. for the Alfisol described in Problem 5 at both ionic
strengths. Compare your results with p.z.s.e. based on 5crH,titr> taking into
account its imprecision. Explain any discrepancy between p.z.n.p.c. and
p.z.s.e.

"7. The table presented here gives values of the slope and y- intercept derived
from linear regression of oh on Aq for the A horizons of four Hawai-
ian Andisols and an Oxisol that constitute a chronosequence on basaltic
parent material.

a. Determine ao for each soil.

b. Interpret the p.z.n.p.c. values for the soils in terms of their properties
and the Jackson-Sherman weathering sequence.

Soil age Organic C

(ky) (g kg 1 ) Clay mineralogy 3 Slope

F>A»Q -1.00 ±0.18

A>F»V>Q -0.84 ±0.07

A>F»V>Q -1.02 ±0.08

K>Gi>F»Q -0.89 ±0.15

K>Gi>Go -1.02 ±0.16

a Abbreviations: A, allophane; F, ferrihydrite; Gi, gibbsite; Go, goethite; K, kaolinite; Q, quartz;
V, vermiculite, including pedogenic chlorite.

(Hint: Review the p.z.n.p.c. values mentioned for soil minerals in
Chapter 2 and for humus in Chapter 3. Consider also the reactions of
humus with soil minerals discussed in the latter chapter.)

*8. Thep.z.c. of a soil low in 2:1 clay minerals is 5.0. After phosphate fertilizer
is applied, the soil retains more adsorbed cations at pH 5 than before.
Offer an explanation for this observation in terms of particle surface
charge concepts.

*9. Potassium fertilizer added to a vermiculitic soils causes the retention of
nitrate by the soil at a given pH value to increase. Offer an explanation
for this effect in terms of particle surface charge concepts.

10. Discuss the statement: "In soils with low quantities of 2:1 clay miner-
als, the greater the degree of desilication (silica removal), the higher the

339 ±5

150

390 ± 14

400

136 ±6

1400

125 ±2

4100

51 ± 1

y-lntercept

mmol c kg~ 1 )

p.z.n.p.c.

51±6

4.5 ±0.3

63 ±2

4.9 ±0.2

92 ±5

6.4 ±0.2

28 ±3

4.5 ±0.1

15 ±4

3.4 ±0.1

194 The Chemistry of Soils

p.z.n.c." Consider both the Jackson-Sherman weathering sequence and
the implications for soil fertility (i.e., for adsorbed ion retention).

11. Prepare a Schindler diagram for the Oxisol described in Problem 1.

12. Prepare a Schindler diagram for Hg + reacting with a soil with a p.z.n.c. =
3 .6. Comment on whether the Hg + adsorption data in the table presented
here imply specific adsorption as a likely reaction mechanism.

Adsorbed Hg

(mmol kg~ 1 )

3.01

50.4

3.20

85.4

3.49

99.0

3.59

115.5

3.70

136.2

3.84

139.5

4.02

144.3

4.37

160.8

4.61

160.4

*13. The fluoroquinolone antibiotic ciprofloxacin (Problem 12 in Chapter 3)
has log Rvalues for protonation equal to 6.3 ±0.1 for its COOH group and
8.6 ± 0.2 for its NH3 group. Prepare a Schindler diagram for ciprofloxacin
reacting with a typical temperate-zone soil and use it to predict whether
ion exchange mechanisms are likely to be operative.

14. For which of the following diprotic organic acids presented in the table
would significant adsorption by the soil described in Figure 7.6 be strong
evidence of specific adsorption mechanisms?

Organic acid log K-i log K 2

Catechol 9.4 12.8

Phthalic 3.0 5.4

Salicylic 3.0 13.7

15. Why is it not usually appropriate to use p.z.n.p.c. instead of p.z.n.c. to
construct a Schindler diagram?

Soil Adsorption Phenomena

8.1 Measuring Adsorption

After reaction between an adsorptive i and a soil adsorbent, the moles of i
adsorbed per kilogram of dry soil is calculated with the standard equation

n; = no; — M w m; (8.1)

where n;x is the total moles of species i per kilogram dry soil in a slurry
(batch process) or in a soil column (flow-through process), as described in
Section 7.2; M w is the gravimetric water content of the slurry or soil column
(kilograms water per kilogram dry soil); and m; is the molality (moles per
kilogram water) of species i in the supernatant solution (batch process) or
effluent solution (flow- through process). (For a discussion of the units of
n;x, M w , and m;, see the Appendix.) Equation 8.1 defines the surface excess,
n;, of a chemical species that has become an adsorbate. Formally, n; is the
excess number of moles of i per kilogram soil relative to its molality in the
supernatant solution. As mentioned in Section 7.2, this excess can be positive,
zero, or negative.

Consider, for example, a Mollisol containing humus and 2:1 clay minerals
that reacts in a batch adsorption process with a CaCi2 solution at pH 7. After
the reaction, the soil and supernatant aqueous solution are separated by cen-
trifugation. The resulting soil slurry is found to contain 0.053 mol Ca kg
and to have a gravimetric water content of 0.45 kgkg -1 . The supernatant
solution separated from the slurry contains Ca at a molality of 0.01 mol kg -1 .

195

196 The Chemistry of Soils
According to Eq. 8.1,

-l

n Ca = 0.053 - (0.45) (0.01) = +0.049 mol kg

is the positive surface excess of Ca adsorbed by the soil. Suppose that the
molality of Cl in the supernatant solution is 0.02 mol kg -1 and that the soil
slurry contains 0.0028 molClkg . Then,

n cl = 0.0028 - (0.45) (0.02) = -0.0062 mol kg -1

is the negative surface excess of Cl adsorbed by the soil. In both examples, n; is
the relative excess moles of species i (per kilogram dry soil) compared with a
hypothetical aqueous solution containing M w kilograms water and species i at
the molality m;. This excess is attributed to the presence of the soil adsorbent.
If the initial molality of species i in the reactant aqueous solution is m?
and the total mass of water in this solution that is mixed with 1 kg dry soil, in
either a batch or a flow-through process, is Mx w , then the condition of mass
balance for species i can be expressed as

m°M Tw = n iT + mi(M T w-M w ) (8.2)

(moles added initially) (moles in slurry) (moles in supernatant solution)

Equations 8.1 and 8.2 can be combined to yield

n ; = AmiM Tw (8.3)

where Am; = m° - m; is the change in molality, attributed to adsorption.
Equation 8.3 is applied frequently to calculate a surface excess as the product
of the change in adsorptive concentration times the mass of water added per
unit mass of dry soil. Note that the right side of Eq. 8.3 refers only to the
aqueous solution phase and that Am; can be positive, zero, or negative. In
practice, the difference between molality and a concentration in moles per
liter can be neglected in applying the equation.

As a second, more complicated example of the use of Eq. 8.1, consider a
montmorillonitic Entisol that contains both calcite and gypsum (Section 2.5).
These soil minerals likely will dissolve to release Ca, as well as bicarbonate and
sulfate, when in contact with an aqueous solution. Suppose the soil is equili-
brated in batch mode with a NaCl/CaCi2 solution, followed by centrifugation
to separate the supernatant solution from a soil slurry with a gravimetric water
content that is 0.562 kg kg -1 . Quantitation of the electrolyte composition in
the slurry and the supernatant solution yields the following data set:

nNaT = 13.20 mmol kg CNa = 12.67 mmol L

ncaT = 79.25 mmol kg -1 cc a = 7.28 mmol L _1

ncrr = 13.90 mmol kg -1 cq = 25.03 mmolL -1

n HC0 3 T = 25.10mmolkg _1 c HC0 3 = 0.27mmolL _1

nso 4 T = 5.00 mmol kg cso 4 = 0.98 mmol L

Soil Adsorption Phenomena 197

where the difference between molality and moles per liter in the supernatant
solution has been neglected. For a montmorillonitic soil, it is reasonable to
assume that the concentrations of bicarbonate and sulfate and, therefore, a
portion of the Ca present, can be attributed mainly to soil mineral dissolution.
Charge balance considerations then would reduce nc a T and cc a according to
the expressions

n CaT - n CaT - -nHC0 3T ~ n so 4T = 61.70 mmol kg -1
c Ca = c Ca - -CHCO3 - c so 4 = 6 - 17 mmol L _1

as a first approximation that neglects the adsorption of the two anions.
By Eq. 8.1, again ignoring the minute difference between molar and molal
concentrations, the respective surface excesses of Na, Ca, and Cl are

n Na = 13.20 - (0.562)12.67 = +6.07 mmol kg -1
n Ca = 61.70 - (0.562)6.17 = +58.23 mmol kg -1
n a = 13.90 - (0.562)25.03 = -0.17 mmolkg -1

The cations are positively adsorbed by the soil under the conditions of mea-
surement, whereas chloride is once again negatively adsorbed, consistent with
the montmorillonitic character of the soil.

8.2 Adsorption Kinetics and Equilibria

Experiments have shown that adsorption reactions in soils are typically rapid,
operating on timescales of minutes or hours, but that sometimes they exhibit
long-time "tails" that extend over days or even weeks. Readily exchangeable
ions (Section 7.2) adsorb and desorb very rapidly, with a rate usually governed
by a film diffusion mechanism (Section 3.3 and Special Topic 3). Specifically
adsorbed ions show much more complicated behavior in that they often adsorb
by multiple mechanisms that differ from those involved in their desorption,
and their rates of adsorption or desorption are described by more than one
equation during the time course of either process. It is usually these ions with
adsorption reactions that will have the long-time tails.

Adsorption kinetics for ions are assumed to be represented mathematically
by the difference of two terms, as in Eq. 4.2:

-£ = R f " R b (8-4)

where Rf and Rf, are forward and backward rate functions respectively.
A consensus does not exist regarding which rate laws should be applied to
model Rf and Rj,. Many different empirical formulations appear in the soil

198 The Chemistry of Soils

chemistry literature. One popular choice has been a rate law like that in
Eq. S.3.7 (Special Topic 3 in Chapter 3):

Rf = k ads c;(n imax -n;) R b = k des n; (8.5)

where n; max is the maximum value of n;, and k ads and k des are the rate coef-
ficients in Eq. S.3.7. As indicated in Table 4.2, appropriate plotting variables
can be identified to determine the rate coefficients under conditions such that
either Rf or Rb is negligible. For example, if desorption alone is provoked
by placing an equilibrated soil in contact with a very dilute aqueous solution
(R f = 0), eqs. 8.4 and 8.5 combine to become a first-order rate law in n;.
The rate coefficient k des is then determined from the slope of a plot of In «;
versus time (Table 4.2). However, rate laws like those in Eq. 8.5 do not reflect
a unique mechanism of adsorption or desorption. They are empirical math-
ematical models with an underlying mechanistic significance that must be
established by independent experiments on the detailed nature of the surface
reactions they purport to describe.

A graph of n; against m; or q at fixed temperature and applied pressure at
any time during an adsorption reaction is an adsorption isotherm. Adsorption
isotherms are convenient for representing the effects of adsorptive concentra-
tion on the surface excess, especially if other variables, such as pH and ionic
strength, are controlled along with temperature and pressure. Figure 8.1 shows
four categories of adsorption isotherm observed commonly in soils.

The S-curve isotherm is characterized by an initially small slope that
increases with adsorptive concentration. This behavior suggests that the affin-
ity of the soil particles for the adsorbate is less than that of the aqueous solution
for the adsorptive. In the example of copper adsorption given in Figure 8.1,
the S-curve may result from competition for Cu + ions between ligands in
soluble humus and adsorption sites on soil particles. When the concentration
of Cu added exceeds the complexing capacity of the soluble organic ligands,
the soil particle surface gains in the competition and begins to adsorb copper
ions significantly. In some instances, especially when "hydrolyzable" metals or
"polymerizable" organic compounds are adsorbed, the S-curve isotherm is the
result of cooperative interactions among the adsorbed molecules. These inter-
actions (e.g., surface polymerization) cause multinuclear surface complexes to
grow on a soil particle surface (Fig. 7.5), producing an enhanced affinity for
the adsorbate as its surface excess increases.

The L-curve isotherm is characterized by an initial slope that does not
increase with the concentration of adsorptive in the soil solution. This type of
isotherm is the effect of a relatively high affinity of soil particles for the adsor-
bate at low surface coverage mitigated by a decreasing amount of adsorbing
surface remaining available as the surface excess increases. The example of
phosphate adsorption in Figure 8.1 illustrates a universal L-curve feature: The
isotherm is concave to the concentration axis because of the combination of
affinity and steric factors.

Soil Adsorption Phenomena 199

Altamont clay loam

pH5.1 25°C

1 = 0.01 M

Cu-j- (mmol m )

L-curve

Anderson sandy

clay loam

pH6.2 25°C

1 = 0.02 M

_i_

100

P_ (mmol m 3 )

1 50 200

0.80 r ,

0.60

0.40

0.20

H-curve

Boomer loam

pH7.0 25°C

1=0.005 M

_1_

_i_

150

curve

/ °

100

0/ o

°/

Har-Barqan clay
parathion adsorption

from hexane
50% RH hydration

i i i

0.05 0.10 0.15 0.20 0.25

Cd T (mmol m d )

C (mmol m J )

Figure 8.1. The four categories of adsorption isotherm as characterized by their
shapes as curves. Abbreviations: I, ionic strength; RH, relative humidity.

The H-curve isotherm is an extreme version of the L-curve isotherm
(an XL-curve). Its characteristic large initial slope (by comparison with an
L-curve isotherm) suggests a very high relative affinity of the soil for an
adsorbate. This condition is usually produced either by inner-sphere surface
complexation or by significant van der Waals interactions in the adsorption
process (sections 3.4 and 3.5). The example of cadmium adsorption shown in
Figure 8.1 illustrates an H-curve isotherm evidently caused by specific adsorp-
tion. Soil humus and inorganic polymers (e.g., Al-hydroxy polymers) can
produce H-curve isotherms resulting from both specific adsorption and van
der Waals interactions.

The C-curve isotherm is characterized by an initial slope that remains
independent of adsorptive concentration until the maximum possible adsorp-
tion is achieved. This kind of isotherm can be produced either by a constant
partitioning of an adsorptive between the interfacial region and the soil solu-
tion, or by a proportionate increase in the amount of adsorbing surface as

200 The Chemistry of Soils

the surface excess increases. The example of parathion (diethyl p-nitrophenyl
monothiophosphate) adsorption in Figure 8.1 shows constant partitioning of
this compound between hexane, a hydrophobic liquid, and the layers of water
on soil particles that accumulate at 50% relative humidity (RH). Similarly,
the adsorption of a hydrophobic organic compound by soil humus is often a
constant partitioning between the latter solid phase and the soil solution as
described by a C-curve isotherm (Section 3.4).

The adsorption isotherm categories illustrated in Figure 8.1 can be
quantified by expressing the data in terms of the distribution coefficient,

K di = rii/Q (8.6)

where c; represents a soil solution concentration of an adsorptive species i.
Equation 3.10 is the special case of Eq. 8.6 obtained by dividing both sides
of the latter expression with the soil organic C content (f oc )- Thus the Chiou
distribution coefficient is simply a distribution coefficient normalized to the
soil organic C content (i.e., K oc = Kd/f oc )- Comparatively, the C-curve corre-
sponds to a distribution coefficient that is independent of the surface excess,
whereas the S-curve corresponds to one that increases initially with the surface
excess. The L- and H-curve isotherms, by contrast, correspond to a distribution
coefficient that decreases with increasing surface excess.

Equation 8.6 necessarily provides a complete mathematical description
of the C-curve isotherm because the left side of the equation is a constant
parameter. The L-curve isotherm usually is described mathematically by the
Langmuir equation:

bKc; , x

(8.7)

1 + Kcj

where b and K are adjustable parameters. The capacity parameter b represents
the value of n; that is approached asymptotically as q becomes arbitrarily
large. The affinity parameter K determines the magnitude of the initial slope
of the isotherm. Equation 8.7 can be derived from the rate law obtained by
combining eqs. 8.4 and 8.5:

-rr = k ads Ci (n max - n ; ) - k des n; (8.8)

Under steady-state conditions, the left side of Eq. 8.8 is zero and Eq. 8.7 follows
upon solving for n; and making the parameter identifications:

b = n max , K = k a ds/kdes (8.9)

Equation 8.9 provides a connection between an empirical rate law and the
Langmuir equation. Note that the affinity parameter K is large if adsorption is
rapid and desorption is slow (i.e., k a d s 2> kd es )- After multiplying both sides of

Soil Adsorption Phenomena 201

Eq. 8.7 by ( 1/c; + K) and solving for Kj;, one finds that the Langmuir equation
is equivalent to the linear expression

K di = bK - Kn;

(8.10)

Thus, a graph of Kj; against n; should be a straight line with a slope equal to
— K and an x-intercept equal to b, if the Langmuir equation is applicable.

Adsorption isotherm equations cannot be interpreted to indicate any
particular adsorption mechanism or even if adsorption — as opposed to
precipitation — has actually occurred. On strictly mathematical grounds, it can
be shown that a sum of two Langmuir equations with its four adjustable
parameters will fit any L- curve isotherm, regardless of the underlying
adsorption mechanism. Thus, adsorption isotherm equations, like rate laws,
should be regarded as curve-fitting models without particular mechanistic
significance, but with predictive capability under defined conditions.

To see this latter point in detail, consider the typical situation in which
the distribution coefficient decreases with increasing surface excess (Fig. 8.2).
If Kj extrapolates to a finite value as the surface excess tends to zero and
extrapolates to zero at some finite value of the surface excess, then adsorption
isotherm data can always be fit to the two-term equation

biKiq b 2 K 2 Ci

1 + Kiq 1 + K 2 c;

(8.11)

1.0

0.8

o
tn

ra 0.6

<" 0.4 -

* 0.2 _

Slope = ex., / a„

Intercept = a n / laJ
Slope = p Q /p 1

(w)

IWJ _i

n p (mmol P kg soil )

Intercept = (3„

Figure 8.2. Plot of the distribution coefficient (Eq. 8.6) for phosphate adsorption by
a clay loam soil, with lines illustrating Eqs. 8.14 and 8.15.

202 The Chemistry of Soils

where t>i, b 2 , Ki, and K2 are empirical parameters, and q is a soil solution
concentration. Equation 8.11 can be derived rigorously, but its correctness as
a universal approximation emerges after using Eq. 8.6 to substitute for q in
terms of K d ; and n; to generate a second-degree algebraic equation (dropping
the subscript i for convenience):

K d + (Kj + K 2 )K d n + KjKjn 2 - (bjKi + b 2 K 2 )K d

-bKiK 2 n = (8.12)

where b = bi + b 2 . Equation 8.10 is recovered if K 2 and b 2 are set equal to
zero. The derivative of K d with respect to n follows from Eq. 8.12 as

dK d = (K 1 + K 2 )K d + 2K 1 K 2 n-bK 1 K 2
dn 2K d +(K 1 + K 2 )n-(b 1 K 1 +b 2 K 2 )

As n tends to zero, K d can be approximated by a linear equation in n, and
Eqs. 8.12 and 8.13 combine to show that

K d R» a + (ai/a )n (n|0) (8.14)

where

a = b 1 K 1 +b 2 K 2 , a 1 = -(b 1 K 2 i +b 2 Kl)

According to Eq. 8.14, the x-intercept of the linear expression is oIq/|oii|, as
indicated in Figure 8.2. As n tends to its maximum value b, K d drops to zero,
according to Eq. 8.12. Thus, K d is once again a linear function of n, and
Eqs. 8.12 and 8.13 can be used to demonstrate that

Kd«(PS/IPil) + (Po/Pi)n (nfb) (8.15)

where

bi b?
Po = b = b 1 + b 2 , p 1 = --±--±

Ki K 2

The slope of the line now is P0/P1 < 0, and its x-intercept is b. If adsorp-
tion data are plotted as in Figure 8.2, then the limiting slopes and the two
x-intercepts can be determined graphically. The four values found can be used
to solve uniquely for the four empirical parameters bi, Ki, b 2 , and K 2 . These
parameters, like those in Eq. 8.7, have no particular chemical significance in
terms of adsorption reactions.

If the distribution coefficient does not extrapolate to a finite value as the
surface excess tends to zero, then the Langmuir equation can be generalized to
a power-law expression known as the Langmuir-Freundlich equation:

b(Kq) p
m = — ^r (0 < P < 1) 8.16

1 + (Kq)P

Soil Adsorption Phenomena 203

where b is the maximum value of n; and K is an affinity parameter analogous
to K in the Langmuir equation, to which it reduces if the exponent P = 1 . The
"linearized" form of Eq. 8.16 is analogous to Eq. 8.10:

bK p -K p ni (8.17)

Equation 8.17 can be applied to determine b and K once fS is known. This
exponent is determined by considering Eq. 8.16 at values of q low enough to
justify the approximation

n; R« Acf (q J, 0) (8.18)

which is termed the van Bemmelen-Freundlich equation. The value of |3 is
then found by a log-log plot of surface excess against soil solution concen-
tration that, if it is linear, yields |3 as its slope. Then n;/Cj can be calculated
with adsorption data and plotted according to Eq. 8.17 to estimate b and K.
A generalization of Eq. 8.16 analogous to that of the Langmuir equation in
Eq. 8.11 also can be made. The resulting six-parameter equation has been
applied successfully to model metal cation adsorption reactions (Section 8.5).
However, no mechanistic interpretation of these adsorption isotherm
models can be had on the basis of goodness-of-fit criteria alone — a conclu-
sion that extends even to determining whether an adsorption reaction has
occurred, as opposed to a precipitation reaction. Not only do the data sets for
this latter reaction yield plots similar to that in Figure 8.2 under a broad variety
of experimental settings, but they also are often consistent with undersatura-
tion conditions because of coprecipitation phenomena (Section 5.3), making
identification of the reaction mechanism even more problematic. When no
molecular-scale data on which to base a decision regarding mechanism are
available, the loss of an adsorptive from aqueous solution to the solid phase can
be termed sorption (Section 7.2) to avoid the implication that either adsorp-
tion or precipitation has definitely taken place. As a general rule, a surface
precipitation mechanism is favored by high soil solution concentrations and
long reaction times in sorption processes.

8.3 Metal Cation Adsorption

Metal cations adsorb onto soil particle surfaces via the three mechanisms
illustrated in Figure 7.4. The relative affinity a metal cation has for a soil
adsorbent depends in a complicated way on soil solution composition,
but, to a first approximation, adsorptive metal cation affinities can be ratio-
nalized in terms of inner-sphere and outer-sphere surface complexation and
diffuse-ion swarm concepts. As discussed in Section 7.2, the relative order of
decreasing interaction strength among the three adsorption mechanisms is
inner-sphere complex > outer-sphere complex » diffuse-ion swarm. In an

204 The Chemistry of Soils

inner-sphere surface complex, the electronic structures of the metal cation and
surface functional group are important, whereas for the diffuse-ion swarm
only metal cation valence and surface charge should determine adsorption
affinity. The outer-sphere surface complex is intermediate, in that valence is
probably the most important factor, but the stereochemical effect of immobi-
lizing a cation in a well-defined complex must also play a role in determining
affinity (e.g., Fig. 7.2).

As a rule of thumb, the relative affinity of a free metal cation for a
soil adsorbent will increase with the tendency of the cation to form inner-
sphere surface complexes. This tendency is correlated positively with ionic
radius (Table 2.1). For a given valence Z, the ionic potential Z/R (Section 1.2)
decreases with increasing ionic radius R. This trend implies that metal cations
with larger ionic radii will create a smaller electrical field and will be less likely
to remain solvated during complexation by a surface functional group. Second,
larger R implies a more labile electron configuration and a greater tendency for
a metal cation to polarize in response to the electrical field of a charged surface
functional group. This polarization is necessary for distortion of the electron
configuration leading to covalent bonding. It follows that relative adsorption
affinity series {selectivity sequences) can be established solely on the basis of
ionic radius (Table 2.1):

Cs+ > Rb+ > K+ > Na+ > Li+(Group IA)
Ba 2+ > Sr 2+ > Ca 2+ > Mg 2+ (Group II A)
Hg 2+ > Cd 2+ > Zn 2+ (Group IIB)

These selectivity sequences, which encompass both Class A and Class B char-
acter (Section 1.2), have been observed often in soil sorption experiments. For
borderline metals (i.e., bivalent transition metal cations), however, ionic radius
is not adequate as a predictor of adsorption affinity, because electron configu-
ration also plays a very important role in the complexes of these cations (e.g.,
Mn 2+ , Fe 2+ , Ni 2+ ). Their relative affinities tend to follow the Irving-Williams
order:

Zn 2+ < Cu 2+ > Ni 2+ > Co 2+ > Fe 2+ > Mn 2+

If a soil adsorbent is dominated by humus, either in particulate form or as a
coating on minerals, Class A and B characters return as useful guides to adsorp-
tion affinity, with Class A metals preferring O-containing surface functional
groups and Class B metals preferring N- or S-containing groups.

If a soil is reacted with a series of aqueous solutions with increasing pH val-
ues while containing a metal cation at a fixed initial concentration, the amount
of metal cation adsorbed by the soil will increase with pH to some maximum
value nM, unless complexing ligands in the soil solution compete overwhelm-
ingly for the metal against surface functional groups. In the absence of soluble
ligand competition, a graph of metal cation adsorbed against pH will have a

Soil Adsorption Phenomena 205

Figure 8.3. Adsorption edges for Pb + , Cu + , and Cd + interacting with poorly crys-
talline Fe(OH)3. The inset shows graphs of the data according to Eq. 8.20 (Kurbatov
plot). Data from Wang, Z.-J., and W. Stumm (1987) Heavy metal complexation by
surfaces and humic acids: A brief discourse on assessment by acidimetric titration.
Netherlands J. Agric. Sci. 35: 231-240.

characteristic sigmoid shape known as an adsorption edge. Adsorption edges
for Pb 2+ , Cu 2+ , and Cd 2+ on freshly precipitated Fe(OH)3, as might be found
in a flooded soil (Section 6.5), are shown in Figure 8.3. Often these curves are
characterized numerically by pH 50 , the pH value at which one half the value
of nM is achieved. It is observed typically that pHso increases as the relative
affinity of the metal cation for the soil decreases. For example, pHso is often
larger for Mn 2+ than Cu 2+ , and larger for Mg 2+ than Ba 2+ . In Figure 8.3 it is
evidently larger for Cd 2+ than for Cu 2+ , and larger for Pb 2+ than for Cu 2+ .
Nearly always, pHso is well below the pH value at which significant hydrolysis
of a metal cation occurs in aqueous solution.

A model equation to describe adsorption edges can be developed if a
semilog graph of the distribution ratio,

D; = n;/(nMi — n;) (adsorptive i)

(8.19)

against pH is linear over a sufficiently broad range of the latter variable.
Semilog graphs of D versus pH demonstrating a linear relationship, known as
a Kurbatov plot,

lnD; = aj + PipH

(8.20a)

are shown in the inset of Figure 8.3 . A geometric interpretation of the empirical
parameters a, f3 in Eq. 8.20a can be made as follows. The pH value at which
half the moles of adsorptive i added are in an adsorbate form is defined as
pHso. Because D; = 1 at this pH value, according to Eq. 8.19, it follows from
Eq. 8.20a that

P H 50 = a i/Pi

5.21)

206 The Chemistry of Soils

Therefore, Eq. 8.20a can be rewritten as

lnDi = Pi(pH-pH 50 ) (8.20b)

or, after combining Eqs. 8.19 and 8.20b, as a model equation for nj,

n; = n Mi {l + exp[-Pi(pH - pHs,,)]}" 1 (8.22)

The sigmoidal curve described by Eq. 8.22 can be interpreted with the help
of a Schindler diagram (Section 7.5). Taking the data plotted in Figure 8.3 as
an example, one can refer to the Schindler diagram for this system shown in
Figure 7.8. The rather narrow range of pH over which Fe(OH)3 can function
as a cation exchanger is apparent, as is the conclusion that specific adsorption
mechanisms must be operating in the reactions of Pb 2+ and Cu 2+ , because
their adsorption edges plateau at pH < p.z.n.c. while the adsorbent surface
is still positively charged. The adsorption edge for Cd , on the other hand,
occurs mainly at pH > p.z.n.c. and, therefore, is consistent with a cation
exchange mechanism.

A comparison of the apparent pHso values for the adsorption edges in
Figure 8.3 with the sequence of -log *K values for the three adsorptive metal
cations shows that the two parameters are correlated positively (i.e., a high pH
value for hydrolysis implies low adsorption affinity). This kind of correlation
has been apparent in many studies of metal cation adsorption by oxyhydroxide
minerals. In conceptual terms, it amounts to a general rule, that metal cations
that hydrolyze at low pH also will adsorb strongly (i.e., will adsorb at pH values
well below their —log *K value) . From a coordination chemistry perspective, the
complexation of a metal cation with OH - in aqueous solution is analogous
to the inner-sphere complexation of the metal cation to an ionized surface
hydroxyl group, with the role of the proton in OH - now being played by
the metal in the adsorbent structure to which the surface hydroxyl is bonded:
= Fe-CT <$■ HO".

8.4 Anion Adsorption

The common soil anions Cl _ and NO^~ adsorb mainly as diffuse-ion swarm
species or as outer-sphere surface complexes. Evidence for this generalization
comes from their readily exchangeable character and the frequent observation
of negative surface excess when they are adsorbed by soils with low p.z.n.c, as
encountered in the examples discussed in Section 8.1. Negative adsorption can
occur only for adsorbate species in the diffuse-ion swarm. On the molecular
scale, this phenomenon can be interpreted through the definition

[c;(x)-coi]dV (8.23)

where q(x) is the concentration (moles per unit volume) of anion i at point
x in the aqueous solution portion of a suspension containing m s kilograms

Soil Adsorption Phenomena 207

of soil, Co; is the concentration of ion i in the supernatant solution, and the
integrals extend over the entire suspension volume. Equation 8.23 actually
applies to any ion in the diffuse swarm. If negative adsorption occurs, q(x) <
Co; and n; < 0. This condition is produced by electrostatic repulsion of the
ion i away from a surface of like charge sign (e.g., an anion in a soil containing
significant humus or minerals with negative structural charge). An estimate of
the average size of the interfacial region over which this repulsion is effective
can be made by defining the exclusion volume:

V e

CiOO

coi

dV/m s = -ni/coi (8.24)

In the first adsorption example discussed in Section 8.1, V ex = 0.0062 mol
kg _1 /20molm- 3 = 3.1 x 10- 4 m 3 kg _1 = 0.31 L kg -1 . (Note that c oi = 0.02
molal ~ 20 mol m -3 .) In suspensions of montmorillonite, this figure could be
an order of magnitude larger for the same chloride concentration. In general,
V ex is the average volume of the region in the soil solution (per kilogram
dry soil) in which q(x) is smaller than its "bulk" value, Co;. The observation
of negative n; and an appreciable V ex is compelling evidence for significant
diffuse-ion swarm species of an anion i.

Oxyanions, most notably arsenate, borate, phosphate, selenite, and car-
boxylate, are usually observed to adsorb as inner-sphere surface complexes.
Several kinds of experimental evidence support this conclusion. Perhaps the
most direct is the often-observed difficulty in desorbing anions like phosphate
by leaching with anions like chloride. Another comparative type of evidence
is the persistence of, for example, borate adsorption at pH > p.z.n.c, whereas
chloride adsorption diminishes rapidly to zero at these pH values. Finally,
spectroscopic methods have led to structural conceptualizations of adsorbed
phosphate, selenite, borate, silicate, and molybdate ions like that shown for
biphosphate shown in Figure 7.3. Although none of these pieces of evidence
may be definitive when taken alone, combined they make a very strong case
for ligand exchange (Eq. 3.12) as a principal mode of oxyanion (excepting
nitrate, perchlorate, selenate, and possibly sulfate) adsorption by soil miner-
als. In general, for an anion A reacting with a Lewis acid site, the reaction
scheme is

=SOH(s) + H+(aq) = =SOH+(s) (8.25a)

=SOH+(s) + A € ~(aq) = =SA (€_1) ~(s) + H 2 0(£) (8.25b)

If the Lewis acid site is present already, or if the concentration of A is very
large, the protonation step in Eq. 8.25a is not required. Ligand exchange is
favored by pH < p.z.n.p.c.

The graphs in Figure 8.4 illustrate the typical effect of pH on positive anion
adsorption by soil particles. Fluoride and borate are representative anions of
monoprotic acids, whereas phosphate represents anions of a polyprotic acid,

208 The Chemistry of Soils

100

£ E

Q- s=

Figure 8.4. Sketches of adsorption envelopes for fluoride, phosphate, and borate
anions. Note the distinct resonance feature in the envelopes for the monoprotic anions
fluoride and borate.

a group that also includes arsenate, arsenite, carbonate, and molybdate. The
monotonic graph of phosphate adsorption versus pH is termed an adsorption
envelope, the inverse of the adsorption edge defined in Section 8.3. It can
be described mathematically by eqs. 8.20 and 8.22 with p 1 ; < and with
the absolute value of P; then being used in Eq. 8.21. A monotonic decrease
in the relative amount of anion adsorbed with increasing pH is observed for
both strongly adsorbing anions and readily exchangeable anions, the difference
between them appearing in the much higher pHso value for anions that adsorb
specifically. If an adsorptive anion does not protonate strongly (e.g., Cl _ , NO^~,
S0 4 ~, and Se0 4 - ), the decrease in ch that always occurs with increasing pH
produces a repulsion of the anion from soil particle surfaces that becomes
dominant at pH > p.z.n.c. Therefore, a positive surface excess will decrease
uniformly with pH, and pHso will lie well below p.z.n.c. If an adsorptive anion
of a polyprotic acid does protonate strongly (e.g., P0 4 ~ and As0 4 - ), it will
adsorb according to the ligand exchange reactions in Eq. 8.25 and the decrease
in an will have less impact (mainly through reversing the reaction in Eq. 8.25a) .
What about strongly adsorbing anions of monoprotic acids? Figure 8.5
shows the effect of pH on a calcareous Entisol reacting with borate in a NaCl
background electrolyte solution. The relevant p.z.n.c. value is 9.5, and log K for
B(OH) 4 protonation is 9.23. The corresponding Schindler diagram, shown in
Figure 7.9, has a top band with a uniformly positive adsorbent surface charge
indicated, a central band with a vertical line at pH 9.2, and a bottom band
with a horizontal line extending over the very narrow range of pH between 9.2
and 9.5. Quite clearly, specific adsorption mechanisms are implicated in the
reaction of borate with the soil. The relatively sharp peak in the adsorption

Soil Adsorption Phenomena 209

Figure 8.5. Adsorption envelope for borate reacting with an Entisol. Data from
Goldberg, S., and R.A. Glaubig (1986) Boron adsorption on California soils. Soil Set.
Soc. Amer. J. 50: 1173-1176.

envelope at a pH value approximately equal to log K for borate protonation,
however, bears scrutiny. At pH values less than 9.2, borate anions do exist
to some degree and are attracted to the positively charged soil adsorbent in
increasing numbers as pH increases from 7 to 9. At pH values more than 9.2, the
adsorptive is predominantly anionic, but now the adsorbent is also becoming
increasingly negatively charged, leading to a sharp fall-off in the adsorption
envelope at pH > p.z.n.c. Thus, the resonance feature in Figure 8.5 can be
interpreted as the net effect of an interplay between adsorptive charge and
adsorbent charge. Because specific adsorption mechanisms play a major role
in the reaction between the adsorptive and adsorbent, however, the resonance
feature will be broadened relative to that resulting from charge relationships
alone (cf. the resonance feature for fluoride in Fig. 8.3). Surveys of available
data indicate that the strength of adsorption of an anion to an oxide mineral is
indeed correlated positively with its log K value for protonation. From a local
coordination perspective, anions that protonate strongly will adsorb strongly,
with the complexation of a proton by the anion in aqueous solution being
analogous to that between the anion and the positive surface site =S + in
Eq. 8.25b. In short, if an anion has a high affinity for the proton, it is expected
to have a high affinity for a Lewis acid site.

8.5 Surface Redox Processes

Soil adsorption processes affect oxidation-reduction reactions in two impor-
tant ways. One of them relates to surface-controlled dissolution reactions in
which an adsorptive forms a surface complex with a metal cation exposed at
the periphery of a mineral (Section 5.1), after which an electron transfer occurs
between the metal and adsorbate prior to the detachment of the complex and

210 The Chemistry of Soils

its subsequent equilibration with the soil solution. Surface-controlled min-
eral dissolution promoted by an adsorptive ligand is illustrated in the lower
half of Figure 5.1, but neither the metal in the adsorbent nor the adsorptive
is redox active in this example (dissolution of gibbsite promoted by fluoride
adsorption). The dissolution of redox-active Fe- and Mn-bearing minerals
is described by several half-reactions listed in the middle of Table 6.1, but
their coupling with the oxidation of a reductant species (e.g., Eq. 6.3 for the
reductive dissolution of goethite) does not necessarily invoke adsorption as an
intermediate step. (See also Problem 10 in Chapter 6.) However, abiotic reduc-
tive dissolution reactions usually involve the formation of surface complexes
that serve as mediators of electron transfer.

Surface- controlled reductive dissolution reactions are distinguished by the
formation of a surface complex between an adsorbent oxidant and an adsorp-
tive reductant that facilitates a redox reaction, which then results in the
dissolution of the adsorbent. Examples of these reactions include the reductive
dissolution of Fe(III)- and Mn(IV)-bearing minerals by biomolecules (e.g.,
ascorbate or citrate) and the reductants in soil humus; by Fe + and Mn + ;
and by a variety of redox-active inorganic species, such as NH^~, H3ASO3,
and HSeO^~. The potential for a surface-controlled reductive dissolution reac-
tion can be examined by first evaluating whether adsorption of the reductant
is favorable, using either a Schindler diagram for the adsorbent-adsorptive
pair or detailed information about specific adsorption of the reductant, then
evaluating whether a redox reaction between the pair has a favorable ther-
modynamic equilibrium constant. For example, similar to the bivalent metal
cations with adsorption edges that appear in Figure 8.3, Mn + is adsorbed by
goethite at alkaline pH (pH 50 ~ 8.7, -log *K = 10.6). Whether the adsorbed
Mn 2+ can then reduce Fe(III) in the adsorbent can be evaluated by considering
the reduction half-reactions (Table 6.1):

FeOOH(s) + 3H+ + e" = Fe 2+ + 2H 2 0(£) (8.26a)

MnOOH(s) + 3H+ + e" = Mn 2+ + 2H 2 0(£) (8.26b)

under the not unreasonable assumption that the oxidation of adsorbed Mn 2+
results in rapid hydrolysis of the consequent adsorbed Mn + (-log *K ~ -0.3
for Mn + ) to form a surface precipitate resembling the mineral manganite.
The overall redox reaction, obtained by combining Eqs. 8.26a and 8.26b after
reversing Eq. 8.26b,

FeOOH(s) + Mn 2+ = MnOOH(s) + Fe 2+ (8.26c)

has log K = -12, according to the data given in Table 6.1. This value of log K
predicts a highly unfavorable reaction (i.e., [Fe + ]/[Mn + ] ~ 10 at equi-
librium, implying a rather low yield of ferrous iron from reactant Mn + ).
The underlying reason for this result can be appreciated by constructing
a redox ladder with "rungs" for the two redox couples: FeOOH/Fe 2+ and

Soil Adsorption Phenomena 211

MnOOH/Mn 2+ (Fig. 6.4). Because pE for the reductive dissolution of FeOOH
lies well below that for MnOOH, electron transfer is favored from the former
couple to the latter couple. Therefore, it is actually the reductive dissolution
of manganite by Fe 2+ that is the favorable reaction. Because p.z.n.c. ~ 6.4
for manganite and -log *K = 9.4 for Fe , a Schindler diagram predicts that
adsorption of the reductant at alkaline pH should be facile, and manganite
should be unstable in the presence of soluble ferrous iron.

Surface-controlled oxidative dissolution reactions are defined similarly to
the reduction reactions, but with the direction of electron transfer reversed.
Examples include the incongruent dissolution of Fe(s) (zero-valent iron,
Section 6.4) by a broad variety of pollutant species (see Problems 8 and 9
in Chapter 6), of green rust (Section 2.4 and Problem 5 in Chapter 6) by a
variety of oxyanions, and of Fe(II)-bearing primary and secondary minerals
by a variety of pesticides and other pollutant compounds. For example, nitrate
reduction (Section 6.2),

1 5 , 1+3 ,

-NO" + -H+ + e" = -NH+ + -H 2 0(£) (8.27a)

8 4 8 8

can be coupled with the oxidative dissolution of chloride-bearing green rust
to form magnetite (Section 2.4),

-Fe 4 (OH) 8 Cl(s) = -Fe 3 4 (s) + e" + -H+ + -H 2 {€) + -Cl" (8.27b)

The overall redox reaction,

^Fe 4 (OH) 8 Cl(s) + ^N0 3 - = ^Fe 3 4 (s) + ^NH++

J O D O

— H+H H 2 0(£) + -C1" 8.27c

20 40 5

has log K = 14.90 + (3/5) [42.7 - (8/3) 18.16] = 11.46, according to the data
given in Table 6.1 and Problem 5 in Chapter 6, taking into account charge and
mass balance as discussed in Special Topic 4 in Chapter 6. Thus, the oxidative
dissolution of green rust by nitrate ions is highly favorable. The adsorption of
nitrate by anion exchange with chloride is the likely first step of this process.
Measurements of the yield of NHJ" and the consumption of Fe(II) for the
reaction in Eq. 8.27c give a NH^ -to-Fe(II) molar ratio in agreement with the
reaction stoichiometry, NH^ /Fe(II) = 1/8 -=- 9/5 = 5/72, because 1 mol green
rust contains 3 mol Fe(II).

Surface oxidation-reduction reactions are abiotic electron transfer pro-
cesses in which the oxidant and reductant interact as adsorbate species
(Fig. 8.6). In this case, the adsorbent does not participate in the redox reaction.
Surface redox reactions are ubiquitous and important agents of transforma-
tion in soils and sediments. Their usual mechanism is a sequence initiated by
inner-sphere surface complexation of either an oxidant or the reductant by an

212 The Chemistry of Soils

edd

Oxidant

-I Reductant J

Figure 8.6. Conceptual scheme for surface oxidation— reduction reactions. The upper
schematic illustrates electron density donation (edd) by a surface anionic site (com-
plexing anion) to a cationic reductant adsorbed on the site. This donation of electron
density enhances the ability of the reductant to transfer electrons (ET) to an oxi-
dant that binds to the reductant to form a ternary complex on the surface. The lower
schematic illustrates electron density donation by an adsorbed anionic oxidant to a
cationic surface site (complexing cation), which then enhances the ability of the oxi-
dant to accept electrons (ET) from a reductant that binds to it to form a ternary surface
complex.

adsorbent. Then a complex forms between the adsorbed species and another
reactant as a precursor to an electron-transfer step, after which this ternary sur-
face complex (Section 7.1) becomes destabilized by the production of reduced
and oxidized species. If the complex formed between oxidant and reductant is
outer-sphere, the electron transfer step is termed a Marcus process, whereas if
it is inner-sphere, the electron-transfer step is termed a Taube process. Electron
transfer is likely to be the rate -limiting step in surface oxidation-reduction
reactions governed by the Marcus process because of the intervening water
molecules in an outer-sphere complex.

An example of a surface redox reaction can be developed by further con-
sideration of Mn 2+ adsorbed on goethite, because the adsorbent is stable
against any reductive dissolution promoted by the adsorbate. A ternary sur-
face complex involving a pair of goethite surface OH, Mn , and O2 will
transform into oxidized Mn [e.g., Mn(III)] and reduced O2 (to form H2O) as
products after electron transfer has occurred:

(=FeO)Mn° + 2 -> (=FeO) 2 Mn° . . . 2 -> products

(8.28a)

Soil Adsorption Phenomena 213

where the dotted line represents O2 bound to adsorbed Mn. This reaction is
analogous to what predominates when Mn(II) is oxidized in aqueous solution:

Mn(OH)° + 2 -> Mn(OH)° • • • 2 -> products (8.28b)

In both reactions, which are thought to involve Taube processes, the presence
of two O-containing ligands in the initial complex with Mn 2+ is required
by the observed pH dependence of the overall redox reaction. These ligands
donate electron density to Mn + and thereby facilitate electron transfer to 2 .
This effect can be seen by comparing the second-order rate coefficients [sec-
ond order because there are two reactants in Eq. 8.28 (Section 4.2)] for the
oxidation of the three species Mn 2+ , Mn(OH)', and (=FeO)Mn°. At 25 °C
they are, respectively, <10 , 20.9, and 0.56Lmol s , which indicates
clearly the great benefit of complexation. Note that this benefit is nearly two
orders of magnitude larger for the soluble complex than for the corresponding
surface complex. This kind of comparison, seen typically in surface redox reac-
tions, evidently reflects the greater electron density donating power of soluble
ligands.

In more quantitative terms, the effect of complexation can be expressed by
the K value for the reduction half-reaction of the redox couple [e.g., MnfOHjj
/Mn(OH)2],as discussed for complexes of iron in Section 6.4. Greater electron
density donation would result in a smaller K value and, therefore, a greater
stability of the oxidant in a redox couple, according to the reasoning given
in Section 6.4. This relationship, in turn, implies that the second-order rate
coefficient for oxidation of the reductant member of the couple will correlate
negatively with K: the smaller K, the more stable the oxidant and the larger the
rate of oxidation of the reductant. This kind of correlation is indeed found.
For the example of Mn(II) oxidation, it implies that K for the soluble com-
plex is smaller than K for the surface complex, because the rate coefficient for
oxidation is larger for the former species. Smallest of all will be the rate coeffi-
cient for Mn + oxidations because water molecules in a solvation complex are
rather weak electron density donors when compared with complexing ligands
such as OH - or =FeO~.

Of course, the adsorbed metal cation need not be Mn 2+ (it could be Fe 2+ ,
for example) and the adsorbed oxidant need not be 2 [it could be Cr(VI)
or U(VI), or even an organic compound]. The basic chemical concept is that
a reductant species is adsorbed and forms a ternary surface complex with
an oxidant species that then becomes unstable against a subsequent electron
transfer. The role of the adsorbent in all this is solely catalytic: that of donating
electron density to the reductant to facilitate its oxidation.

For that matter, the species bound directly to the adsorbent need not be
a reductant. An oxidant could be adsorbed, then form a ternary surface com-
plex with a reductant (Fig. 8.6). For example, HCrO^~ could be adsorbed and
subsequently form a complex with an organic reductant (e.g., phenol) that
then becomes unstable against electron transfer, with the result that Cr(III)

214 The Chemistry of Soils

is formed and the organic compound (e.g., a phenol or oxalate) is oxidized.
In this case, a ligand exchange mechanism and formation of an inner-sphere
surface complex by the oxidant (Eq. 8.25) will withdraw electron density from
it and thereby facilitate electron transfer to it from the reductant it later com-
plexes. This effect is analogous to that of protonation of an oxidant in aqueous
solution, which is well-known to enhance electron transfer reactions (more
so, typically, than does surface complexation, in consonance with the similar
trend for adsorbed reductants). Once again, the adsorbent plays only a cat-
alytic role: that of withdrawing electron density from the oxidant to facilitate
its reduction.

For Further Reading

Bidoglio, G., and W. Stumm (eds.). (1994) Chemistry of aquatic systems. Kluwer
Academic Publishers, Boston. Chapters by L. Charlet and by A. Stone,
K. L. Godtfredsen, and B. Deng in this edited volume provide excellent
overviews of adsorption phenomena and surface oxidation-reduction
reactions respectively.

Essington, M. E. (2004) Soil and water chemistry. CRC Press, Boca Raton, FL.
Chapter 7 in this comprehensive textbook gives a discussion of adsorption
phenomena in soils quite parallel to but more detailed than that in the
current chapter.

Huang, P. M., N. Senesi, and J. Buffle (eds.). Structure and surface reactions of
soilparticles John Wiley, Chichester, UK. The twelve chapters of this edited
monograph provide an advanced survey of soil adsorption reactions,
including spectroscopic methods and chemical modeling.

Sparks, D. L., and T. J. Grundl (eds.). Mineral-water interfacial reactions. Amer-
ican Chemical Society, Washington, DC. This symposium publication
offers an eclectic, advanced discussion of specialized approaches to nat-
ural particle surface chemistry that extend the concepts discussed in the
current chapter.

Sposito, G. (2004) The surface chemistry of natural particles. Oxford University
Press, New York. Chapter 3 of this advanced textbook discusses
the kinetics of specific adsorption, reductive dissolution, and surface
oxidation-reduction reactions.

Problems

The more difficult problems are indicated by an asterisk.

1. Dry soil (350 mg) is mixed with 20 mL of a solution containing 4.00 mol
m -3 KNO3 at pH 4.2. After equilibration for 24 hours, a supernatant
solution is collected and found to contain 3 .96 mol m -3 KNO3 . Calculate

1.87

25.39

28.11

3.06

34.14

77.68

9.19

37.34

155.1

Soil Adsorption Phenomena 215

nK and nN0 3 for the soil, in millimoles per kilogram. What is the p.z.n.c.
of the soil?

2. The data in the table presented here refer to Cu(II) adsorption by
an Aridisol. Plot an adsorption isotherm with the data and classify it
according to the criteria discussed in Section 8.2.

n Cu (mmol kg 1 ) c Cu (mmol m 3 ) n Cu (mmol kg 1 ) c Cu (mmol m 3 )

6.87
10.64
18.05

3. Analyze the data in the following table [chlortetracycline (CT, an
antibiotic) adsorption by an Alfisol] to classify the adsorption isotherm.

ncT(|J-mol kg 1 ) cct(m-tioI m 3 ) ncKM-mol kg 1 ) ccT(M- m °l m 3 )

59
119
231

4. Calculate Kj as a function of nc u for the data in Problem 2, then select an
isotherm equation to fit the data. Calculate the isotherm parameters and
estimate the 95% confidence intervals for them.

5. Analyze the data in the table [Cd(II) adsorption by an Alfisol] to show
that the van Bemmelen— Freundlich isotherm equation is appropriate to
describe them. Calculate the parameters A and p 1 and their 95% confidence
intervals.

n Cc |(mmol kg 1 ) c Cc j(mmol m 3 ) n Cc j(mmol kg 1 ) c Cc j(mmol m 3 )

0.11
0.30

0.53

"6 a. Express K<j formally as a function of n to first order in a Taylor series,
then derive Eqs. 8.14 and 8.15 using Eqs. 8.12 and 8.13.
b. Show that Eq. 8.16 leads to an infinite value of Kj as the surface
excess tends to zero.

521

1025

0.89

0.61

4.45

1.78

0.79

12.5

3.56

1.14

17.8

216 The Chemistry of Soils

7. Plot an adsorption edge for Mg(II) on an Oxisol based on the data in the
table presented here. Calculate pHso given a maximum adsorption of 8
mmol kg -1 at pH 6. Evaluate the applicability of Eq. 8.20.

n Mg (mmol kg 1 )

nMg(

mmol kg 1 )

0.72

2.48

2.45

3.36

1.08

2.73

3.64

3.80

1.80

3.05

4.21

4.10

2.14

3.20

6.35

5.00

8. Estimate pHso values for the adsorption edges in Figure 8.3 and perform
a linear regression analysis of the relationship between pHso and -log *K
for the three metal cations. What value of pHso, including an error of
your estimate, is predicted for Mn 2+ ?

"9. Analyze the data in the table presented here (negative adsorption of
Cl _ by a temperate-zone soil) to determine a power-law relationship
between V ex and the concentration of chloride in the supernatant solu-
tion. Mathematical modeling of negative adsorption in the diffuse-ion
swarm based on Gouy-Chapman theory and Eq. 8.24 leads to the
equation

V ex = 2a s /(pc) 1/2

where P = 1.084 x 10 16 m mol -1 (at 25 °C) is a constant model param-
eter and a s is specific surface area. Does the exponent in the power-law
relationship you found agree with the model equation? If it does, apply
the equation to estimate the specific surface area of the soil.

V ex (10- 3 m 3 kg- 1 ) c d (mol m" 3 ) V ex (10- 3 m 3 kg~ 1 ) c a (mol nrr 3 )

1.06
1.00
0.70
0.68

0.55

10. Plot an adsorption envelope for nitrate on an Oxisol using the data in the
table presented here. Extrapolate the data to estimate nMN0 3 > then test the
applicability of Eq. 8.20 (with Pno 3 < 0).

0.79

0.50

6.2

1.1

0.49

6.8

2.0

0.38

7.7

3.1

0.29

9.9

4.0

0.24

20.5

Soil Adsorption Phenomena 217

nNo 3 (mmol kg 1 )

6.6 ±0.3
5.1 ± 1.0

4.7 ±0.7
4.3 ±0.8
4.0 ±0.1

n N o 3 (mmol kg 1 )

2.5

3.5 ±0.3

3.9

2.8

3.0 ±0.3

4.1

3.2

1.5 ±0.2

4.6

3.6

1.2 ±0.6

4.9

3.7

0.6 ±0.2

5.3

11. Simon [Simon, N. S. (2005). Loosely-bound oxytetracycline in riverine
sediments from two tributaries of the Chesapeake Bay. Environ. Sci. Tech-
nol. 39:3480.] has extracted sorbed oxytetracycline, an antibiotic used in
agriculture, from contaminated bay sediments using 1 mol dm -3 MgCi2
solution adjusted to pH 8. The molecular structure of oxytetracycline is
shown in Simon's Figure 2. Over what range of pH should the antibiotic
be a cation? A neutral species? An anion? How would the mechanism of
extraction using MgCbi likely differ in each range of pH? Why does Simon
refer to the extracted antibiotic as "easily desorbed oxytetracycline?"

* 12. It is a common observation that the adsorption edge for a bivalent metal

cation (e.g., Zn 2+ ) on a soil mineral is shifted upward at low pH and
downward at high pH after the mineral becomes coated by humus. Sketch
a typical adsorption edge for a bivalent metal cation and a typical adsorp-
tion envelope for humus on a soil oxyhydroxide mineral, then develop a
mechanistic explanation for this observation.

* 13. When the antibiotic ciprofloxacin (Problem 12 in Chapter 3, Problem 13

in Chapter 7) is in the presence of MnC>2, the antibiotic disappears from
solution and Mn 2+ begins to appear in solution. The rate of antibiotic
loss decreases as pH increases, but increases with the initial concentration
of both the antibiotic and the Mn oxide. Discuss the hypothesis that the
loss of the antibiotic results from a surface- controlled reductive dissolu-
tion reaction. What additional experiments would be useful for testing
the hypothesis? (Hint: Begin by preparing a Schindler diagram for the
antibiotic reacting with the Mn oxide.)

*14. Can the phenol hydroquinone (1,4-benzenediol; Eq. 6.15) be expected to
provoke the surface-controlled reductive dissolution of birnessite? (Hint:
Follow the approach outlined for manganite and Fe 2+ in Section 8.5.)

*15. The second-order rate coefficient (kL, in liters per mole per second) for
Cr(VI) reduction by Fe(II) is found to be related to the pEL value for a
Fe(III)L/Fe(II)L couple (Eq. 6.20) by the equation

logk L = 8.13 -0.60pE L

218 The Chemistry of Soils

a. Give a mechanistic interpretation of the decrease of log kr, with
increasing pEL-

b. The value of kL for Cr(VI) reduction by adsorbed Fe(II) is about

8 x 10 3 L mol -1 s _1 . What is the pE value for the =Fe(III)/=Fe(II)
couple? How does it compare with that for FeOH + /FeOH + ? Give a
mechanistic interpretation as part of your comparison.

Exchangeable Ions

9.1 Soil Exchange Capacities

The ion exchange capacity of a soil is the maximum number of moles of
adsorbed ion charge that can be desorbed from unit mass of soil under
given conditions of temperature, pressure, soil solution composition, and
soil-solution mass ratio. In Section 3.3, a similar definition of the CEC of
soil humus is stated and, in Chapter 8, the surface excess of an ion is related to
the soil chemical factors that affect ion exchange capacities. In many applica-
tions, ion exchange capacity refers to the maximum positive surface excess of
readily exchangeable ions, as defined in Section 7.2. These ions adsorb on soil
particle surfaces solely via outer-sphere complexation and diffuse-ion swarm
mechanisms (see Fig. 7.4).

Measurement of an ion exchange capacity typically involves replacement
of the native population of readily exchangeable ions by an index cation or
anion, then determination of its surface excess following the methodology
discussed in Section 8.1. Detailed laboratory procedures for this measurement
are described in Methods of Soil Analysis (see "For Further Reading" at the
end of this chapter). For soils in which the readily exchangeable cations are
monovalent or bivalent (e.g.,Aridisols), the index cation can be Na + or Mg ,
whereas for soils also bearing trivalent readily exchangeable cations (e.g., Spo-
dosols), K + or Ba 2+ is an index cation of choice (see also Section 3.3). Often
NHJ" has been used as an index cation. Because this cation forms inner-
sphere surface complexes with 2:1 layer- type clay minerals, like that shown
for K + in Figure 7.4, and because it can even dissolve cations from primary

219

220 The Chemistry of Soils

soil minerals, the use of NHJ" to measure the soil CEC has potential for inac-
curacy. The index anion of choice is typically ClO^~, Cl _ , or NO^~. Thus, for
example, MgCl2 could be selected as an index electrolyte for displacing readily
exchangeable ions (see also Problem 1 1 in Chapter 8) . A common modification
of direct displacement of the native population of readily exchangeable ions
is displacement after prior saturation of a soil adsorbent with an indifferent
electrolyte (Section 7.4), such as NaCl04 or LiCl.

A quantitative definition of ion exchange capacity can be developed in
terms of the surface excess and charge balance concepts. Consider first a soil
in which a net positive surface excess of anions is highly unlikely (e.g., the
montmorillonitic Entisol discussed in Section 8.1). Suppose that the only
adsorbed ions in this soil are Na + , Ca 2+ , and Cl _ . Then the CEC of the soil is
defined by the charge balance condition

n NaT + 2n Ca T - n c iT - CEC = (9.1)

where n;x (i = Na, Ca, or Cl) is the total moles of ion i per kilogram dry soil
in a wet soil, as in Eq. 8.1. Equation 9.1 quantifies the role of soil particles
bearing adsorbed cations as being on the same chemical footing as anions in
the soil. The operational meaning of Eq. 9.1 is apparent, given a methodology
for extracting the adsorbed ions, but its quantitative relation to the surface
excess requires substitution of Eq. 8.1 for each participating ion:

CEC = (n Na + M w m Na ) + 2(n Ca + M w m Ca ) - (n c i + M w m c i)
= n Na + 2n Ca - n cl + M w (m Na + 2m Ca - m cl )
= n Na + 2n Ca - n cl = q Na + q Ca - qci (9.2)

where electroneutrality of the soil solution is invoked to eliminate the
molalities and

qi = IZiln; (9.3)

is the adsorbed ion charge of species i. Now, the right side of Eq. 9.2 is equal
to Aq in Eq. 7.2. Thus, CEC is the net adsorbed ion charge evaluated under the
condition that the net adsorbed anion charge is not a positive quantity. Returning
to the example of the Entisol in Section 8.1, we can calculate its CEC as

CEC = 6.07 + 2(58.23) - (-0.17) = 122.7 mmol c kg" 1

Note that the negative surface excess of Cl _ still contributes to the CEC.
Formally, this is required by the condition of charge balance in Eq. 9.1, given
the definition of the surface excess, but mechanistically it is a reflection of the
fact that anion repulsion by a negatively charged particle surface is equivalent
to cation attraction by the surface for species adsorbed in the diffuse-ion
swarm.

The operational nature of CEC should not be forgotten. If a large con-
centration of the index cation is used in a solution at high pH (e.g., >8.2),

Exchangeable Ions 221

Table 9.1

Representative cation exchange capacities (in moles of charge per
kilogram) of surface soils. 3

Soil order

CEC

Soil order

CEC

Alfisols

0.15 ± 0.11

Mollisols

0.24 ±0.12

Andisols

0.31 ±0.18

Oxisols

0.08 ±0.06

Aridisols

0.18 ± 0.11

Spodosols

0.27 ±0.30

Entisols

0.20 ±0.14

Ultisols

0.09 ±0.06

Histosols

1.4 ±0.3

Vertisols

0.50 ±0.17

Inceptisols

0.21 ±0.16

"Based primarily on data compiled in Table 8.2 of Essington, M. E. (2004). Soil
and water chemistry. CRC Press, Boca Raton, FL. CEC = cation exchange capacity.

the measured surface excess of the index cation should approximate closely
the absolute value of the maximum negative intrinsic surface charge of a
soil (Section 7.3). On the other hand, if the pH value or some other chem-
ical property of the solution containing the index cation is arranged such
that the maximum negative intrinsic surface charge is not neutralized by the
adsorption of the index cation, then the measured surface excess of the lat-
ter will simply reflect the chemical conditions chosen. An example of this
latter situation appears in Problem 1 of Chapter 7 for Na + adsorption by
an Oxisol under varying pH and ionic strength. Both the maximum and the
less than maximum CEC are useful in soil chemistry. The maximum neg-
ative intrinsic surface charge indicates the potential capacity of a soil for
adsorbing cations, whereas a less than maximum negative intrinsic surface
charge indicates the actual capacity of a soil for adsorbing cations under given
conditions.

Table 9.1 lists representative CEC values for 1 1 soil orders, based primar-
ily on measurements made using NHJ" as the index cation in a solution at
pH 7. High variability of the CEC within each soil order is evident, but the
very low values for Ultisols and Oxisols and the high values for Histosols and
Vertisols are significant trends. Detailed studies of the CEC show that it is cor-
related positively with the content of humus, clay content, and soil pH, if an
unbuffered solution containing the index cation is used in the measurement.
The basis for the correlation with humus content — reflected dramatically in
Table 9.1 by the CEC reported for Histosols — can be understood at once
after comparison of the CEC values of humic substances (5— 9mol c kg ,
Section 3.3) with those for clay minerals like smectite and vermiculite (0.7-
2.5mol c kg _1 , Section 2.3). The correlation with pH is understandable after
reviewing the pH dependence of the net proton charge in Figure 3.3. Indeed,
the pH dependence of a measured less than maximum intrinsic surface charge
should mirror that of the adsorbed index ion charge (see Problems 1 and 3 in
Chapter 7).

222 The Chemistry of Soils

The composition of readily exchangeable ions in a soil can be determined
by chemical analysis of the soil solution after reaction of the soil with index
ions such as Li + and ClO^j - . In alkaline soils, the readily exchangeable cations
are Ca 2+ , Mg 2+ , Na + , and K + , decreasing in their contribution in the order
shown. In acidic soils, the most important readily exchangeable metal cation is
Al 3+ , followed by Ca 2+ and Mg 2+ . Readily exchangeable Al(III), which likely
includes Al 3+ , AlOH + , Al(OH)+, and AlSO^", can be measured by using K + as
an index cation in an unbuffered KCl solution. The remaining exchangeable
metal cations can then be determined by replacement with Ba .

Comprehensive data compilations like those in Table 9.1 are not well
established for the anion exchange capacity (AEC) of soils. The AEC tends
to be important mainly for Spodosols, Ultisols, and Oxisols. Among these
soil orders, AEC values in the range 1 to 50mmol c kg are representative.
A quantitative definition of AEC is developed by generalizing Eq. 9.1. Consider
the Oxisol discussed in Problem 1 of Chapter 7. Because both index ions
have positive surface excess in this soil, the charge balance condition must be
expressed in the form

nNaT - n c iT + AEC - CEC = (9.4)

Invoking the definition of the surface excess in Eq. 8.1, we can then derive the
equation

qNa - qci = CEC - AEC (9.5)

as a generalization of Eq. 9.2. Evidently, AEC in the soil simply equals qci
under given conditions of pH and ionic strength, with a maximal value near
10mmol c kg at pH 2.6 and I = 30molm . Similarly, CEC is the same as
qNa> reaching about 9 mmol c kg atpH5 andl = 30molm . More generally,
in the absence of negative adsorption,

Aq ex = CEC - AEC (9.6)

where

Aq ex = oos + era (9.7)

defines a special case of Eq. 7.2 appropriate to readily exchangeable ions.
Equation 9.6 shows that the net adsorbed ion charge of readily exchangeable
ions equals the difference between CEC and AEC. If it is known that anions
are actually negatively adsorbed by a soil, then AEC is dropped from Eq.
9.6 and it reduces to Eq. 9.2 (under the conditions given for the exam-
ple). If it is known that cations are negatively adsorbed by a soil, then
CEC is dropped from Eq. 9.6. In either of these special cases, negative sur-
face excess still contributes to the ion exchange capacity, as in the Entisol
example.

Exchangeable Ions 223

9.2 Exchange Isotherms

An exchange isotherm is analogous to an adsorption isotherm (Section 8.2),
except that the variables plotted are charge fractions instead of surface excesses
and soil solution concentrations. The charge fraction of an adsorbed ion is
defined by

Ei = qi/Q (9.8)

where Q is the sum of adsorbed ion charges for each ion that undergoes
exchange with ion i:

Q = E k 1k (9-9)

The charge fraction of an ion in aqueous solution is defined similarly as

Ej = IZilmiQ (9.10)

where m; is the molality (or other concentration variable) of ion i and

Q = J] k |Z k |m k (9.11)

An exchange isotherm, then, is a graph of E; against E; under the same fixed
conditions that apply to an adsorption isotherm. Evidently, the maximum
range of a charge fraction is from zero to one.

Exchange isotherms for Ca — > Mg exchange at pH 7 are illustrated in
Figure 9.1 for two 2:1 clay minerals and two soils — a Vertisol and an Aridisol —
with clay fractions that are dominated by the minerals indicated. One of the
variables kept constant during the bivalent cation exchange reactions described
by the isotherms was the charge fraction of adsorbed Na + (Ejvja)- Thus, the
isotherms refer to both binary and ternary exchange systems. In natural soils,
of course, ternary, quaternary, or even higher order exchange systems are
the norm. A binary exchange reaction such as Ca — > Mg is still useful for
detailed laboratory study, however, but only under the critical assumption that
naturally occurring, higher order n-ary exchange systems can be understood
in terms of component binary exchange reactions. That this assumption may
be true is indicated by the closeness of the exchange isotherms in Figure 9.1,
which suggests that Ca — > Mg exchange on the clay minerals and soils is largely
independent of the presence of adsorbed Na + in the E^a range investigated.
Note that both Q and Q are limited to contributions from Mg 2+ and Ca 2+ to
allow direct comparison with binary exchange data (ENa = 0).

The solid lines in Figure 9.1 are thermodynamic nonpreference exchange
isotherms. For bivalent-bivalent exchange, and for any other exchange reaction
involving ions having the same valence, the thermodynamic nonpreference
isotherm is represented mathematically by the simple equation

E; = Ej (9.12)

224 The Chemistry of Soils

1.0

0.8

0.6

0.4

0.2
f ° (

"iLI

1.0
0.8
0.6
0.4
0.2

1 1 ->

Ca — ^-Mg Exchange W
— Montmorillonite ^ -

pH7

E Na =0.00 •
E Na =0.16 •

/ 1

E Na =0.36 o

I I

1 1 ! J 1 1 I

Ca — »-Mg Exchange

I I

Altamont Soil

pH7

- E Na =0.00 .

- E Na =0.10 •

1 i

■ E Na =0.22 °

— —

>* I I I I I I

1.0
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

1 1 1 r

-Ca — *-Mg Exchange
lllite

— i — i 1 — i — r

Ca-Mg Exchange
-Domino Soil o

PH7 *

3 '°E Na =0.00.
Em„ = 0.23 o

_1_

_J_

-L

-l_

0.2 0.4 0.6 0.8 1.0

Figure 9.1. Exchange isotherms for Ca —> Mg exchange at 25 °C on montmorillonite
and a Vertisol (Altamont series), and on illite and an Aridisol (Domino series). Charge
fractions were calculated considering only the surface excess and aqueous solution
concentration of Ca and Mg, irrespective of whether Na was present. The thermo-
dynamic nonpreference isotherm (Eq. 9.12) is indicated by a solid line. Data from
Sposito, G.,C. Jouany, K.M. Holtzclaw, andC.S. LeVesque (1983) Calcium-magnesium
exchange on Wyoming bentonite in the presence of adsorbed sodium. Soil Sci. Soc.
Amer. J. 47:1081-1085; Fletcher P, Holtzclaw KM, Jouany C, Sposito G, and LeVesque
CS (1984) Sodium-calcium-magnesium exchange reactions on a montmorillonitic
soil: II. Ternary exchange reactions. Soil Sci. Soc. Amer. J. 48:1022-1025; Sposito, G.,
C.S. LeVesque, and D. Hesterberg (1986) Calcium-magnesium exchange on illite in the
presence of adsorbed sodium. Soil Sci. Soc. Amer. J. 50:905—909.

which plots as a straight line that makes a 45° angle with both the x- and
y-axes. On both montmorillonite and illite, the Ca — > Mg exchange appears
to show no preference for either cation at pH 7 and over the range of ENa
investigated. On the Vertisol (Atamont soil) this also may be true, although
the data do appear to lie very slightly below a nonpreference line, indicating
that Ca + may be slightly favored over Mg + in the exchange reaction. The
situation for the Aridisol (Domino soil) is more clear: The data lie well below
a nonpreference line, more so perhaps in the ternary system (E^a = 0.23).
These differences between the soils and the corresponding clay minerals may

Exchangeable Ions 225

reflect the presence of humus, where carboxyl groups tend to have a greater
affinity for Ca + than for Mg + because of the larger radius of the former
cation (see Section 8.3).

For monovalent-bivalent exchange, the nonpreference isotherm is
described by a more complicated equation:

Ebb

A(l - E biv ) 2
Ebiv+A(l -E biv ) 2

(9.13)

where Ebi v is the adsorbed charge fraction of the bivalent cation and A =
QYmono^Ybiv with y being a single-ion activity coefficient (Eq. 4.24). The
curve resulting from Eq. 9.13 is illustrated in Figure 9.2 for Na — > M 2+
exchange (M = Ca or Mg) under the conditions Q = 0.05mol c L and
y^/ybiv = 1.5, so that A = 0.0375. If E biv = 0.2, then, by Eq. 9.13,
Ebi v = 1 — (0.024/0.224)5 = 0.67, which agrees numerically with the solid
curve in the figure. The derivation of Eq. 9.13 is outlined in Section 9.3.
Suffice it to say here that the derivation is based on two assumptions: (1)
the thermodynamic equilibrium constant for the exchange reaction has unit
value and (2) the adsorbed cations behave as an ideal solid solution in the soil
(Section 5.3).

According to Figure 9.2, which shows two more exchange isotherms for the
Domino soil, the Ca and Mg isotherms lie above the nonpreference isotherm,

1.0

50 mol m
pH7

Perchlorate

0.3 0.4

Bivalent

0.6

Figure 9.2. Exchange isotherms at 25 ° C for Na — > Ca and Na — > Mg exchange on the
Aridisol featured in Figure 9.1. The thermodynamic nonpreference isotherm is also
indicated (Eq. 9.13).

226 The Chemistry of Soils

indicating selectivity of the soil for bivalent cations relative to Na + , which has
the lesser valence. Evidently there is more of a selectivity difference between
Ca 2+ and Na + than Mg 2+ and Na + . This latter difference agrees with the
Ca — > Mg isotherm in the lower right quadrant of Figure 9.1. Note, however,
that these conclusions depend on the chemical conditions under which the
exchange reactions occur. The parameter A in Eq. 9.13 is related directly to the
electrolyte concentration, such that Eb; v increases as Q decreases for a fixed
E),j v . Therefore, a comparison like that in Figure 9.2 for Q = 0.05 mol c L _1
may change completely as Q changes to higher or lower values. As a general
rule, when Q increases, the nonpreference isotherm for monovalent-bivalent
ion exchange becomes more like a straight line (i.e., more like the nonpref-
erence isotherm for homovalent ion exchange). Thus, decreasing Q or, more
concretely, dilution of the aqueous solution containing the adsorptive ions will
inevitably lead to a greater charge fraction of the adsorbed bivalent ion at a
given value of Et,j v , even though the adsorbent actually exhibits no preference
for the bivalent cation over the monovalent cation. This trend is known as the
Scofield dilution rule.

9.3 Ion Exchange Reactions

As stated in Section 9.1, the usual meaning of ion exchange reaction in soil
chemistry is the replacement of one readily exchangeable ion by another. On the
molecular level, this means that ion exchange is a surface phenomenon involv-
ing charged species in outer-sphere complexes or in the diffuse-ion swarm.
In practice, this conceptualization is adhered to only approximately. Cation
exchange reactions on soil humus, for example, include protons (Section 3.3)
that may be adsorbed in inner-sphere surface complexes. Common extracting
solutions for CEC measurements (e.g., NH4C2H3O2 or BaCi2) may displace
metal cations from inner-sphere surface complexes as well as readily exchange-
able metal cations. Development of experimental methods that will quantitate
only readily exchangeable ions or will partition adsorbed ions accurately into
readily exchangeable and specifically adsorbed species remains the objective
of ongoing research.

Ion exchange reactions on whole soils or soil separates (e.g., the clay
fraction) cannot be expressed as chemical equations that show the detailed
composition of the adsorbent. Soil adsorbents are very heterogeneous and,
therefore, an approach similar to that used to describe cation exchange on
soil humus (Section 3.3) must be adopted. The symbol X will denote the soil
adsorbent in the same way that =SO was used to denote the humus adsorbent.
This representation is meant to depict the ion exchange characteristics of soil
only in some average sense, with chemical equations for ion exchange written
by analogy with expressions like Eqs. 3.2 through 3.4. For example, the Na + — >
Ca 2+ exchange reaction underlying some of the data in Figure 9.2 can be

Exchangeable Ions 227

expressed as

Na 2 X(s) + Ca 2+ = CaX(s) + 2 Na+ (9.14a)

2 NaX(s) + Ca 2+ = CaX 2 (s) + 2 Na+ (9.14b)

2NaX(s) + Ca 2+ = 2 Cai X(s) + 2 Na+ (9.14c)

Equation 9.14 illustrates three alternative ways to represent the same cation
exchange reaction. In Eq. 9.14a, X denotes an amount of soil bearing 2 mol
intrinsic negative surface charge (cf. Eq. 3.2), whereas in Eqs. 9.14b and 9.14c,
X - denotes an amount of soil bearing 1 mol intrinsic negative surface charge
(cf. Eq. 3.3). As long as the amount of intrinsic surface charge is made clear, X
can be used in either case as the symbol for the soil adsorbent, and in neither
does the "valence" —1 or —2 have any molecular significance. Equation 9.14c
differs from Eq. 9.14b by emphasizing that it is 1 molCa charge that reacts with
1 mol soil adsorbent charge. Thus Eq. 9.14b is expressed in terms of the moles
of Ca and Na that react with 1 mol X, whereas Eq. 9.14c is expressed in terms
of the moles of Ca and Na charge that react. The choice of which equation
to use is a matter of personal preference, because both equations satisfy basic
requirements of mass and charge balance (see Special Topic 1 in Chapter 1).

The kinetics of ion exchange can be described quantitatively in terms
of the concepts developed in Special Topic 3 (Chapter 3) for adsorption-
desorption reactions of cations. Essential to this approach is the decision
regarding whether the rate-controlling step is diffusive transport or surface
reaction. A variety of data suggests that rates of ion exchange processes often
are transport controlled, not reaction controlled. This is patently true if the ions
involved merely replace one another in the diffuse-ion swarm (Section 7.2).
Thus, readily exchangeable ions most probably engage in reactions with rates
that are transport controlled, whereas specifically adsorbed ions participate
in reactions that are surface controlled (Table 9.2). Adsorption reactions that
involve both solvated and unsolvated adsorbate species (e.g., the exchange
of Na + in the diffuse-ion swarm for K + that forms an inner-sphere surface
complex on a 2:1 clay mineral) could exhibit rates that are influenced by both
diffusion and the kinetics of surface complexation reactions.

Even with diffusion taken as the rate-limiting process for ion exchange
reactions, there remains a need to distinguish between film diffusion and
intraparticle diffusion (the latter being ion diffusion into the pore space of
an aggregate, with subsequent adsorption onto pore walls). This can be done
experimentally by an interruption fesf.When an ion exchange reaction has been
initiated, the adsorbent particles are separated physically from the aqueous
solution phase, then are reimmersed in it after a short time interval. If film
diffusion is the rate-limiting step, no significant effect of this interruption on
the kinetics should be observed. If intraparticle diffusion is the rate-limiting
step, the concentration gradient driving the ion exchange process should drop
to zero during the interruption, and the rate of ion exchange should increase

228 The Chemistry of Soils

Table 9.2

Comparing ion exchange with specific adsorption.

Property

Surface species

Ion exchange

Outer- sphere surface
complexes and
diffuse-ion swarm

Adsorptive charge versus Always opposite

surface charge

Kinetics Transport control

Cation affinity Increases with Z and R a

Anion affinity

Increases with |Z| and R

a Abbreviations: R, ionic radius; Z, ionic valence.
b Equation 7.14.

Specific adsorption

Inner-sphere surface
complexes

Either opposite or the

same

Surface control

Increases with log *K for

hydrolysis

Increases with log K for

protonation

after the exchanger particles are reimmersed in the aqueous solution phase,
causing a gradient to be reestablished. In general, soil particles with large
specific surface areas should favor film diffusion, whereas those with significant
microporosity should favor intraparticle diffusion.

Equation S.3.8 in Special Topic 3 is a model rate law for transport-
controlled adsorption of a cation i by a univalent charged site, =SO~.
Adopting the convention in Eq. 9. 14b for cation exchange (i.e., = SO - •<=>• X - )
and considering the example of Li + — > Na + exchange on a soil adsorbent, we
can apply Eq. S.3.8 to both cations under the condition of equilibrium with
respect to their adsorption reactions (rate = 0) to derive the ratio

[Na+]

k Na /k Na [NaX]
des ' ads L J

t Li+ ] l&/l&[LiX]

(9.15a)

where the subscript bulk has been dropped to simplify notation. Equation
9.15a can be rearranged to form the expression

[NaX][Li+] _ kaA£ _ T ...i-N:.
[LiX][Na+] ]£/]£

(9.15b)

The parameter defined by ratios of rate coefficients is a conditional equilibrium
constant (Section 4.2) for the cation exchange reaction:

LiX(s) + Na+ = NaX(s) + Li +

(9.16)

Slightly generalized to replace concentrations with the activities of Li + and
Na + in aqueous solution (Eq. 4.20), it is known as the Vanselow selectivity

Exchangeable Ions 229
coefficient

M.-s,_ [NaX](Li+)
[LiX](Na+)

Ky ^ a = :;;;;;;;;\; (9.15c)

(Note that yjjj a = y£j if Eq. 4.24 is used to calculate activity coefficients.)

Equation 9.15c is a model expression for an equilibrium constant to
describe the reaction in Eq. 9.15b. In general, the ratio on the right side of
Eq. 9.15c will not remain constant as the relative amounts of NaX(s) and
LiX(s) change under varying aqueous solution composition; hence, it defines
a conditional equilibrium constant, as discussed in Section 4.5. When the ratio
on the right side of Eq. 9.15c does remain constant, the adsorbate is said to
be an ideal solid solution comprising NaX(s) and LiX(s). This designation is
consonant with the definition of an ideal solid solution given in Section 5.3,
because [NaX]/[LiX] is equal to the stoichiometric ratio of NaX to LiX in
the adsorbate and would be replaced by the activity ratio (NaX) to (LiX) if
Ky were a true thermodynamic equilibrium constant. Thus, the Vanselow
selectivity coefficient is an ion exchange equilibrium constant derived according
to the ideal solid solution model of a soil adsorbate.
Equation 9.15b also can be written in the form

K v i/Na = ^^ (9.15d)

EljENa

where the charge fractions E; and E; (i = Na or Li) are defined in Eqs. 9.8 and
9.10 respectively. A rearrangement of Eq. 9.15d to solve it for ENa yields

„Li/Na p

ENa= K I, /Na ENa - (9-17)

1 + (K v l/Na - l)E Na

after noting that El; = 1 — E^ and El; = 1 — E^a- The Li — > Na exchange
reaction is said to be selective for Na + if K v > 1 and selective for Li +

if Ky < 1. The corresponding graphs of E^ versus ENa — exchange

isotherms — will be convex toward the y-axis and convex toward the x-axis
respectively, in keeping with these definitions of selectivity. If Ky = 1, there
is said to be no preference for either cation, and the resulting exchange isotherm,
equivalent to Eq. 9.12 with i = Na, is the thermodynamic nonpreference
exchange isotherm. It plots as a straight line.

A Vanselow selectivity coefficient also can be developed for the Na — > Ca
exchange reaction in Eq. 9.14b:

K Na/Ca = XCafNa^

4 a (Ca 2 +)

230 The Chemistry of Soils

where x Ca = [CaX 2 ]/([CaX 2 ] + [NaX]) and x Na = [NaX]/([CaX 2 ] + [NaX])
= 1 — xca are termed the mole fractions of CaX 2 and NaX 2 in the adsorbate.
(Note that the mole fraction ratio x^a to xy appears in Eq. 9.15c.) Like the

Na/Ca

selectivity coefficient for Li — > Na exchange, the value of K v usually is not
constant as the composition of the adsorbate changes, but Eq. 9.18 still can
be used as a guide to selectivity. Upon introducing the definitions of charge
fractions,

Eca = qca/Q = 2[CaX 2 ]/(2[CaX 2 ] + [NaX]) = 1 - E Na
E Ca = 2[Ca 2+ ]/Q = 2[Ca 2+ ]/(2[Ca 2+ ] + [Na+]) = 1 - E Na (9.19)
and noting Eq. 4.20, one generalizes Eq. 9.13:

(A/Kv v " ■"") II -he,' 1

E C a= 1

Na/Ca. / £ \2

LE C a+(A/Kr" a )(l-Eca) Z J

(9.20)

Na/Ca

When K v = l,Eq. 9.20 reduces to the nonpreference isotherm in Eq. 9.13,
with biv being Ca in this special case. If K ' > 1, the exchange isotherm
will lie above the curvilinear nonpreference isotherm, showing selectivity for
Ca (or, more generally, biv), as in Figure 9.2. In this way, model expressions
like Eqs. 9.18 and 9.20 permit the interpretation of exchange isotherms for
univalent — > bivalent ion exchange in soils of arbitrary texture and compo-
sition. The Vanselow model, however, is not necessarily a realistic description
of the adsorbate in ion exchange reactions, but serves instead as both a use-
ful approximation on which to base a semiquantitative understanding of these
reactions as they occur in soils and a reference model for defining ion exchange
selectivity.

9.4 Biotic Ligand Model

The biotic ligand model is a simplified chemical approach to characterizing
the acute toxicity of borderline and Class B metals (Section 1.2) to organisms
living in natural waters, sediments, or soils. (Acute toxicity refers to the effect
on an organism caused by exposure to a single dose of a toxicant chemical over
a period of time ranging from 24 to 96 hours.) The purpose of the model is
to evaluate quantitatively the manner in which water and soil chemistry affect
the short-term bioavailability of a toxic metal under conditions typical of
acute toxicity tests, as implemented in environmental toxicology laboratories.
Thus, the organisms considered with respect to toxic effects usually are those
commonly used in such tests, and the primary goal of a biotic ligand model is
to provide quantitative input into the development of water and soil quality
criteria based on standard acute toxicity data. These data almost always are total
concentrations of a toxicant that cause either death or significant impairment

Exchangeable Ions 231

of the functioning of test organisms deemed by ecotoxicological practice to be
reliable indicator species (see Problem 13 in Chapter 3). Although originally
developed for application to aquatic organisms, the biotic ligand model has
been extended to describe metal toxicity to microbes and plant roots in soils.
Biotic ligand models may differ regarding which mathematical formula-
tion is used to describe dose-response relationships, or regarding how toxicant
chemical species are identified and quantified, but they all invoke the same set
of three hypotheses as their toxicological foundation. A comprehensive intro-
duction to the biotic ligand model is given in a review article by Paquin et al.
[Paquin, P. R., et al. (2002) The biotic ligand model: A historical overview.
Comp. Biochem. Physiol. Part C 133:3.]

1. The free toxicant metal ion activity (section 4.3 to 4.5) in a natural water
or the soil solution is determined by the chemical reactions depicted in
the competition diagram shown in Figure 1.2. The timescales of these
reactions are assumed to be incommensurate with the timescale of an
acute toxicity test (i.e., other chemical forms of the toxicant metal than
the free-ion species either have already equilibrated with it or can be
assumed so kinetically inhibited as not to occur on the timescale of the
toxicity test).

2. Toxic effects of a metal on a test organism are correlated positively with
the concentration of the free metal ion species that is complexed by a
ligand that is characteristic of the test organism, a so-called biotic ligand.
Thus, a test organism (e.g., a species of microbes or roots in Figure 1.2,
or of crustaceans, algae, or fish in a natural water) is assigned a
metal-binding site analogous to those on soil particle surfaces. No
assumption is made about the identity or molecular structure of the
biotic ligand. However, it is assumed to react directly with free metal ion
species in the aqueous solution phase contacting the test organism. In
keeping with Hypothesis 1, the timescale for this reaction is very short
when compared with that for toxic response.

3. Toxic response depends only on the fraction of binding sites on the
biotic ligand that are occupied by the free-ion species of the toxicant
metal. This fraction is determined by the competing reactions pictured
in Figure 1.2 and by competition for the biotic ligand itself from other
free-ion species (e.g., protons and Class A or B metals).

A biotic ligand model necessarily makes use of chemical speciation calcu-
lations as outlined in sections 4.3 and 4.4, but with pertinent precipitation-
dissolution and adsorption— desorption reactions (chapters 5 and 8) included
along with complexation reactions. All the caveats discussed in Section 4.4
apply to these calculations as well, so they must be borne in mind when the
biotic ligand model is applied in a regulatory context. Adding to the approxi-
mate nature of the model is the characterization of adsorption reactions with

232 The Chemistry of Soils

particle surfaces, of which metal ion binding by the biotic ligand is one:

M m+ + =BL"(s) = =BLM (m-1) (s) (9.21)

by analogy with the notation used to depict a reactive surface site in Special
Topic 3 (Chapter 3), where =BL~(s) is a biotic ligand site that adsorbs a metal
cation M m+ . A conditional equilibrium constant for the reaction in Eq. 9.21
can be written by analogy with Eq. 4.7:

[^BLM^" 1 )]

KcMBL = , 9.22

[M m +][ = BL -]

By Hypotheses 1 and 2, K c mbl an d the conditional equilibrium constants for
all of the reactions portrayed in Figure 1.2 along with those between the biotic
ligand and the cations that compete with M m+ determine [=BLM( m_1 )], the
concentration that correlates with toxic response.

Hypothesis 3 requires consideration of the speciation of the biotic ligand
following the example in Eq. 4.13:

=BL T = [=BL - ] + [=BLM (m_1) ] + [BLH°]

+ [=BLNa°][=BLCa + ]H (9.23)

with H + , Na + , and Ca + exemplifying competing cations. Of particular
interest is the species distribution coefficient c(=blm :

= [^BLM^" 1 )] = K cM BL[M m +]

«=BLM - =BLt - {1 + KcMBL[M m +] + K cHB l[H+] + • • •}

(9.24)

with a method of derivation that is described in Section 4.3. This distribution
coefficient is introduced into a suitable dose-response expression to develop
the predictive machinery of the model. It is evident from Eq. 9.24 that, in
the absence of competing cations, the relation between c(=blm an d [M m+ ]
is analogous to the Langmuir isotherm equation (Eq. 8.7) and that, in the
presence of competing cations, a=BLM is smaller than when they are absent.
(Note that the impact of each competing cation is the product of an intensity
factor and a capacity factor, as discussed in connection with Eq. 4.18.) Thus,
by Hypothesis 3, the effect of cation competition is to diminish toxic response.
Also according to Hypothesis 3, a unique value of a=BLM is associated with
LC50 or any other concentration of the toxicant metal that causes a defined
toxic effect (LC50 is the concentration that causes 50% mortality among the
organisms used in an acute toxicity test; see Problem 13 in Chapter 3). This
assertion implies that the conditional equilibrium constants in Eq. 9.24 do
not vary with solution composition, an approximation similar to that made
in the Vanselow model of ion exchange. Indeed, ratios of K c mbl to the other

Exchangeable Ions 233

conditional equilibrium constants in Eq. 9.24 describe competition in terms
of the cation exchange reactions

=BLH°(s) + M m+ = =BLM+(s) + H+ (9.25a)

=BLNa°(s) + M m+ = =BLM+(s) + Na+ (9.25b)

=BLCa+(s) + M m+ = =BLM+(s) + Ca 2+ (9.25c)

and so on, in complete analogy with Eq. 9.15b. In this sense, cation exchange
reactions (with = BL _ <=>• X - ) determine the extent to which the biotic ligand
will adsorb M m+ and promote toxic effects on short timescales.

Validation of the biotic ligand model is performed both qualitatively and
quantitatively. For example, at fixed pH and concentrations of competing
metal cations, a LC50 value should increase with increasing dissolved humus
concentration (organic complexes in Fig. 1.2) and, at fixed pH and humus
concentration, it should also increase with increasing concentrations of com-
peting cations. The first trend is a result of another ligand competing with the
biotic ligand for M m+ , whereas the second trend is a result of metal competi-
tion from sites on the biotic ligand, both leading to a reduced value of a=BLM
and, therefore, the need for a higher total concentration of M to cause a given
percent mortality.

A more quantitative test of the model is provided by measurements of
toxic effect in terms of the concentration of the free-cation species M m+ .
According to Eq. 9.24,

[M m+ ] "

=blm/K CmbL [i + KcHbl[h+] + KcNaBL [Na+] + • • •] (9.26)

1 — «=BLM

Equation 9.26 implies that the concentration of M m+ causing a given toxic
effect will increase linearly with the concentration of any competing cation,
provided that Hypothesis 3 is accurate and that the conditional equilibrium
constants do not vary significantly with solution composition. Hypothesis 3
can be examined indirectly, of course, by measuring mortality percentages or
another toxic effect under varying total concentrations of metal M and testing
goodness-of-fit for a proposed mathematical relationship between toxic effect
and a=BLM- A growing body of toxico logical literature attests to the usefulness
of a=BLM as a quantitative measure of acute toxicity, despite the simplifications
inherent to the use of Eq. 9.24.

9.5 Cation Exchange on Humus

One of the most important reactions in Figure 1.2 that determines the free-
ion concentration of an element in the soil solution is adsorption by particle
surfaces, particularly where the surfaces comprise acidic organic functional
groups in humus. These groups are not only more numerous (per unit mass)

234 The Chemistry of Soils

than those found on the surfaces of mineral particles (Section 3. 3), but also are
more complex in terms of molecular structure because of the supramolecular
nature of humic substances, which constitute the major portion of humus
(Section 3.2). This molecular-scale complexity poses a key challenge to quan-
titative modeling of cation exchange reactions that is parallel to that mentioned
in connection with metal speciation calculations in Section 4.4: how to formu-
late metal cation interactions with humus carboxyl and phenolic OH groups
to express the bound metal concentration in terms of conditional stability
constants and free-ion concentrations.

Humic substances, whether dissolved or particulate, exhibit a variety of
molecular-scale environments clustered together in a morass of organic ten-
drils and spheroids with labile conformations that depend on conditions of
temperature, pressure, pH, and soil solution composition. Faced with this
daunting heterogeneity, the modeling of metal complexation by these materi-
als becomes an exercise constrained by parsimony, with the foremost challenge
of striking a balance between the number of chemical parameters necessary to
describe chemical speciation accurately and the varieties of functional group
reactivity with metal cations that must be considered, even for just two classes
of acidic group. One approach that shows promise for applications to soil
solutions is the NICA-Donnan model. (NICA is the acronym for nonideal
competitive adsorption.)

This model appears in Problem 6 of Chapter 3 for the specific application
of describing an and ANC of humic acid. The model expression for an con-
tains two terms, one for each class of acidic functional group. It is convenient,
in making an acquaintance with the NICA-Donnan model, to restrict atten-
tion initially to just one such class. Then the equation for the moles of proton
charge complexed by humus is

. . , [(K H c H )fa]P

qH(cH) = b H (9.27)

1 + [(K H c H ) te ]P

where ch is the concentration of protons in the aqueous solution phase near
the adsorbent surface and Kh is an affinity parameter analogous to K in the
Langmuir equation (Eq. 8.7). According to the definitions given in Prob-
lem 7 of Chapter 3, the quantity qn is the same as the total acidity of the
class of functional groups to which it applies and cth is then equal to the
difference between total acidity (qH) and CEC (bn). Applying these defini-
tions to the NICA-Donnan expression for qn, one finds an equation for an
that is identical in mathematical form to each of the two terms in the model
equation discussed in Problem 6 of Chapter 3. Equation 9.27 is a version
of the Langmuir-Freundlich equation (Eq. 8.16) discussed in Section 8.2. Its
adjustable parameters are Kh, Ph» and p, the latter two of which arise from a
factorization of the exponent |3 in Eq. 8.16. If PhP = 1> then Eq. 9.27 reduces
to the Langmuir equation.

Exchangeable Ions 235

Using the NICA— Donnan model, Eq. 9.27 is to be applied only to com-
plexed protons. Protons adsorbed in the diffuse-ion swarm are accounted for
by a version of surface charge balance as expressed in Eq. 7.5:

CT p + V ex ^] i Z i (c i -c io ) = (9.28)

where the sum is over all species in the diffuse-ion swarm (not only protons)
with valence Z; and concentration q. This latter variable is identified as the
average concentration of an ion i in the exclusion volume V ex near the adsor-
bent surface (Eq. 8.24). Thus, V ex represents the volume of aqueous solution
(per unit mass of adsorbent) that encompasses the diffuse-ion swarm that
balances the net total particle charge a p (Eq. 7.4). The second term on the
right side of Eq. 9.28 is the net adsorbed charge contributed by the diffuse-ion
swarm, given q as the bulk aqueous solution concentration of ion i, as in
Eq. 8.24.

As indicated in Problem 9 of Chapter 8, V ex is found to be inversely
proportional to the inverse square root of c for a given ionic species. More
generally, in log-log form,

log V ex = a - - log I (9.29)

where V ex is in liters per kilogram, I is ionic strength in moles per liter
(Eq. 4.22), and a is an adjustable parameter to be determined from mea-
surements of the ionic strength dependence of the exclusion volume. The
value of a ~ —0.53 ± 0.03 — statistically the same as the coefficient of log I in
Eq. 9.29 — has been established in this way for a variety of humic substances.
Equations 9.27 (with one such equation for each class of acidic functional
group), 9.28, and 9.29 constitute a mathematical model for proton adsorption
by humic substances. The resulting optimized parameters, based on a large
number of proton titration curves (Fig. 3.3) for humic and fulvic acids, are:

bi (mol c kg l ) log Ki

pi b 2 (mol c kg l ) log K 2 p 2

Fulvic acid 5.88 2.34
Humic acid 3.15 2.93

0.38 1.86 8.60 0.53
0.50 2.55 8.00 0.26

in the notation of Problem 6 in Chapter 3, which drops the subscript H and
combines the product PhP into a single exponent, p. (The results given here
for humic acid also appear in Problem 6 of Chapter 3.) Note that the values of
(bi + b 2 ) fall well into the range of CEC typical for humic substances, that the
same is true for b 2 and phenolic OH content, and that log Ki and log K 2 do
not differ substantially between the two types of humic substance, whereas b i
does. The association of carboxyl groups with Ki and phenolic OH with K 2 is
facile.

236 The Chemistry of Soils

Cation exchange is brought into the NICA-Donnan model by expanding
Eq. 9.27 to include a metal cation M:

N , (Kiq)Pi [(K H c H ) fe + (K M c M ) pM ] p

qi(CH)CM) = bj —

(K h c h ) Ph + (K m c m ) Pm 1 + [(K H c H ) te + (K m cm) Pm ] p

(9.30)

where i = H or M and the additional parameters are interpreted analogously to
those inEq. 9.27. The full model equation is actually the sum of two terms like
that in Eq. 9.30 (!), one for carboxyl groups and one for phenolic OH groups.
This equation is complemented by eqs. 9.28 and 9.29 (with q in Eq. 9.28
equated to q in Eq. 9.30) in all applications. After multiplication by the solids
concentration of humic substance (in kilograms per cubic decimeter), the right
side of the equation becomes a molar concentration that can be substituted
directly into a mass balance expression for the metal M as posed in a typical
chemical speciation calculation (see, for example, Eq. 4.6).

The first factor on the right side of Eq. 9.30 is the maximum moles of
proton or metal cation charge that can be complexed by the class of acidic
functional group to which it applies. Experience with the model shows that
this parameter, as would be expected, is proportional to the CEC of the acidic
functional group (bn), with the proportionality constant being the ratio of P;
to Ph- The exponents p; (i = H, M), which take on values between and 1,
thus are relative stoichiometric parameters accounting for differences between
H and M in respect to how many moles of ion charge are bound to one
mole of acidic functional groups. (Thus, Ph was implicitly set equal to one
in applying Eq. 9.27, leaving only the exponent, p.) The second factor on the
right side then gives the fraction of complexes with the acidic functional group
that contain the species i (i = H or M). (Note its similarity to Eq. 9.24.) The
model affinity parameters for these two species are Kh an d Km respectively.
They play the role of conditional stability constants, although no specific
chemical reaction is associated with either of them in the model. A detailed
discussion of these points and, more generally, the complete derivation of the
NICA-Donnan model are given in a review article by Koopal et al. [Koopal,
L. K., T. Saito, J. P. Pinheiro, and W. H. van Riemsdijk. (2005) Ion binding
to natural organic matter: General considerations and the NICA-Donnan
model. Colloids Surf. 265A:40.], whereas a clear overview of the model is given
by Merdy et al. [Merdy, P., S. Huclier, and L. K. Koopal. (2006) Modeling metal-
particle interactions with an emphasis on natural organic matter. Environ. Sci.
Technol. 40:7459.].

The first two factors on the right side of Eq. 9.30 combine to describe
a capacity factor for the complexation of species i (i = H or M). The third
factor in the expression is an intensity factor that models the competition
between protons and metal cations for complexation by a class of acidic func-
tional groups. It contains a "smearing out" parameter, p, with values also
between zero and one, that accounts for intrinsic variability in the affinity

Exchangeable Ions 237

of the groups for either protons or metal cations caused by molecular-scale
effects, such as local electrostatic fields created by the dissociation of groups
near a group that has complexed a proton or metal cation, stereochemistry, or
conformation. This kind of variability can in fact be represented mathemati-
cally by a distribution of affinity parameters with a median value that is K; (i
= H or M) and with a breadth that is represented by the parameter p, with
breadth increasing as p becomes smaller. This is similar to the interpretation of
the exponent P in the Langmuir— Freundlich and van Bemmelen-Freundlich
equations (Section 8.2).

Cation adsorption in the diffuse-ion swarm, including contributions from
a background electrolyte, is considered only in Eq. 9.28. Ionic strength effects
thus are assumed to be produced as a result of screening of the net proton
charge by the background electrolyte cations (Section 7.2). Attracted by neg-
ative charge as quantified by a p (= an), these cations diffuse in from the bulk
electrolyte solution to approach dissociated acidic functional groups, with
most of them swarming near the periphery of the humic substance within a
distance of about 1 nm along an outward direction into the vicinal aqueous

Cd-H Adsorption

on Peat Humic Acid ^£r

pH4

KN0 3

0.01 M

•P ' rP £

•

0.01 M
0.1 M
0.1 M

I I I I

log [Cd 2+ ] (mol dm" 3 )

Figure 9.3. Log-log plot of adsorption isotherms for Cd + at 25 °C on a peat humic
acid at two pH values and two ionic strengths (KNO3 background electrolyte). The
curves (dashed and solid lines) are corresponding plots of the adsorption isotherms
predicted by the NICA-Donnan model. Data from Kinniburgh, D. G., et al. (1996)
Metal binding by humic acid: Application of the NICA-Donnan model. Environ. Sci.
Technol. 30:1687-1698.

238 The Chemistry of Soils

solution. Lateral diffusive motions of the cations following this periphery are
not restricted because the cations do not form complexes, but the electrostatic
field created by the negative charge is diminished in strength by the diffuse
swarm of cations that screens it. The picture here is roughly analogous to that
of an electron cloud screening the nuclear charge in an atom.

Figure 9.3 shows an application of the extended version of Eq. 9.29 to
describe the concurrent adsorption of protons and Cd 2+ by a peat humic acid.
The curves through the data points for two values of pH and ionic strength
(KNO3 background electrolyte) were calculated with a = -0.57 in Eq. 9.29
and the parameter values:

Ioni logKi; Pi, logK 2i P 2 ;

H 2.98 0.86 8.73 0.57

Cd 0.10 0.81 2.03 0.48

bi = 2.74 mol c kg -1 pi = 0.54 b 2 = 3.54 mol c kg -1 p 2 = 0.54

Note that, as a result of cation exchange, qcd is decreased by increasing I and
decreasing pH.

For Further Reading

Di Toro, D. M., H. E. Allen, H. L. Bergman, J. S. Meyer, P. R. Paquin, and
R. C. Santore. (2001) Biotic ligand model of the acute toxicity of metals.
Environ Toxicol. Chem. 20:2383-2396. This review article gives a criti-
cal discussion of the biotic ligand model that takes the reader through
each step typical of model development, with special emphasis given to
calibrating chemical speciation calculations involving humus.

Essington, M. E. (2004) Soil and water chemistry. CRC Press, Boca Raton, FL.
Chapter 8 in this comprehensive textbook gives a discussion of cation
exchange in soils with many examples and careful development of the
concept of the selectivity coefficient.

Milne, C. J., D. Kinniburgh, W. H. van Riemsdijk, and E. Tipping. (2003)
Generic NICA— Donnan model parameters for metal— ion binding by
humic substances. Environ. Sci. Technol. 37:958-971. This article gives
a critical compilation of NICA— Donnan model parameters for metal
cations interacting with humic and fulvic acids.

Sparks, D. L. (ed.). (1996) Methods of soil analysis: Part 3. Chemical methods.
Soil Science Society of America, Madison, WI. Chapters 40 and 41 of this
standard reference describe tested laboratory methods for measuring ion
exchange capacities and selectivity coefficients.

Sposito, G. (1994) Chemical equilibria and kinetics in soils. Oxford University
Press, New York. Chapter 5 of this advanced textbook provides a compre-
hensive discussion of the kinetics and thermodynamics of ion exchange
reactions.

Exchangeable Ions 239

Sposito, G. (2004) The surface chemistry of natural particles. Oxford University
Press, New York. Chapter 4 of this advanced textbook contains a detailed
description of the NICA— Donnan model as applied to cation adsorption
by humic substances.

Problems

The more difficult problems are indicated by an asterisk.

1. After consulting Methods of Soil Analysis (listed in "For Further Reading"),
discuss and compare the BaCi2 (see also Section 3.3) and NH4C2H3O2
methods of measuring CEC as applied to a variable-charge soil (e.g.,
Spodosol or Oxisol).

2. Consult Methods of Soil Analysis to obtain details of the CaCi2/Mg(N03)2
and BaCi2 methods of measuring CEC in soils. Compare the advantages
and disadvantages of each method as applied to a soil with a mineralogy
that reflects the early stage of Jackson-Sherman weathering (Table 1.7).

3. Calculate a conditional exchange equilibrium constant for the reaction
MgX 2 (s) + Ca 2+ = CaX 2 (s) + Mg 2+ based on the data in the table

presented here. Plot K v against Ec a - (Assume that single-ion activ-

ity coefficients can be calculated with the Davies equation.) Does the
adsorbent exhibit preference?

c Mg

Cca

°,Mg

qca

c Mg

Cca

°,Mg °,Ca

(mol

m- 3 )

(mol,

: kg 1 )

(mol

rrr 3 )

(mol c kg" 1 )

20.4

2.4

0.21

0.078

10.1

12.3

0.093 0.21

17.8

4.8

0.17

0.11

4.9

17.0

0.053 0.26

14.8

7.2

0.14

0.15

2.4

19.6

0.027 0.31

12.4

9.7

0.12

0.17

1.2

20.9

0.016 0.30

"4. Show that the use of mole fractions in Eq. 9.18 is consistent with the
assumption that the soil adsorbate is an ideal solid solution. (Hint:
Reinterpret Eqs. 5.28c and 9.15c in terms of mole fractions and then
reformulate the definition of an ideal solid solution.)

5. Plot an exchange isotherm like those in Figure 9.2 using the composition
data on Na — > Ca exchange in the table presented here. Include a non-
preference isotherm based on Eq. 9.13. (Take Q = 0.05 mol c kg and
calculate single-ion activity coefficients with Eq. 4.24 for an ionic strength
of 0.05 mol L _1 .)

240 The Chemistry of Soils

rriNa

m Ca

qNa

qca

rriNa

m Ca

qNa

qca

(mol

kg- 1 )

(mol c

kg- 1 )

(mol

kg- 1 )

(mol c

kg- 1 )

0.0480

0.000136

0.100

0.037

0.0450

0.00164

0.047

0.103

0.0474

0.000320

0.074

0.056

0.0441

0.00212

0.039

0.108

0.0469

0.000717

0.060

0.081

0.0397

0.00475

0.016

0.121

0.0457

0.00118

0.049

0.095

0.0302

0.00976

0.009

0.134

m Na

m Mg

qNa

qMg

(mol

kg- 1 )

(mol,

: kg" 1 )

0.0340

0.0124

0.10

0.74

0.0291

0.0149

0.08

0.74

0.237

0.0174

0.06

0.78

0.0185

0.0197

0.06

0.95

6. Plot an exchange isotherm like those in Figure 9.2 using the data on Na
—> Mg exchange in the table presented here. Show that the isotherm is
essentially a nonpreference isotherm, as described in Section 9.2. (Take
Q = 0.05 mol c kg and calculate single-ion activity coefficients with Eq.
4.24 for I = 0.05 mol L _1 .)

m Na m Mg qNa qMg

(mol kg -1 ) (mol c kg- 1 )

0.0495 0.00117 0.53 0.28

0.0474 0.00234 0.30 0.45

0.0440 0.00700 0.22 0.70

0.0383 0.00940 0.23 0.86

"7. The data in the table presented on the next page show adsorbed cation
charge resulting from the reaction between mixed perchlorate salt solu-
tions (Q = 0.05 mol c L _1 ) and the silt plus clay fraction of a Vertisol
containing 26 ± 7 g C kg in addition to a high content of montmo-
rillonite. Use appropriate statistical methods to determine whether a pH
dependence exists for (a) CEC, (b) E^a* or (c) preference for Ca. (Hint:
Consider plotting each of the properties to be tested against EMg for each
pH value, then follow with linear regression analyses.)

8. Derive Eq. 9.24b for a biotic ligand that binds a toxic metal M 2+ and
the competing cations H + , Ca 2+ , and Mg 2+ , beginning your derivation
with Eq. 9.23. Describe a method to test Hypothesis 3 of the biotic ligand
model with the equation you derive.

9. A fundamental premise of the biotic ligand model is that acute toxic effect
is correlated positively with the concentration of the uncomplexed (free)
toxicant species in aqueous solution. Therefore, acute toxicity may be
expressed in terms of the free species concentration that results in a loss
of function or death (EC50 orLCso) for half a population of test organisms

Exchangeable Ions 241

q Na (mol c kg 1 ) q Ca (mol c kg 1 ) q Mg (mol c kg 1 )

pH 4.7 ±0.3

0.16 ±0.03 0.000 0.46 ±0.02

0.16 ±0.04 0.0897 ±0.0007 0.391 ± 0.006

0.16 ±0.03 0.16 ±0.01 0.342 ±0.009

0.17 ±0.03 0.206 ±0.004 0.304 ± 0.007

0.15 ±0.06 0.251 ±0.007 0.255 ± 0.009

0.15 ±0.04 0.298 ±0.004 0.202 ± 0.005

0.17 ±0.03 0.34 ±0.01 0.148 ±0.006

0.14 ±0.02 0.386 ±0.007 0.116 ±0.004

0.13 ±0.04 0.393 ±0.008 0.074 ± 0.004

0.15 ±0.03 0.43 ±0.01 0.042 ± 0.002

0.13 ±0.04 0.470 ±0.002 0.000

pH 5.8 ±0.1

0.183 ±0.006 0.000 0.481 ±0.003

0.187 ±0.007 0.100 ±0.001 0.412 ± 0.003

0.165 ±0.002 0.159 ±0.001 0.352 ± 0.002

0.160 ±0.005 0.2148 ±0.0002 0.303 ± 0.0003

0.184 ±0.003 0.266 ±0.001 0.256 ±0.001

0.176 ±0.005 0.315 ±0.001 0.210 ±0.001

0.156 ±0.006 0.352 ±0.003 0.161 ±0.003

0.153 ±0.007 0.400 ±0.001 0.120 ±0.001

0.16 ±0.01 0.439 ±0.003 0.0789 ± 0.0003

0.16 ±0.02 0.480 ±0.001 0.044 ± 0.003

0.166 ±0.004 0.522 ±0.005 0.000

pH 6.9 ±0.2

0. 144 ± 0.004 0.552 ± 0.003 0.000

0.146 ±0.003 0.500 ±0.005 0.0501 ± 0.0006

0.146 ±0.006 0.459 ±0.006 0.098 ±0.001

0. 150 ± 0.003 0.409 ± 0.003 0. 144 ± 0.002

0.155 ±0.003 0.358 ±0.004 0.196 ±0.002

0.154 ±0.002 0.317 ±0.002 0.243 ± 0.002

0.156 ±0.004 0.268 ±0.003 0.299 ± 0.002

0.156 ±0.003 0.211 ±0.002 0.346 ± 0.005

0.191 ±0.004 0.154 ±0.002 0.406 ± 0.005

0. 159 ± 0.003 0.0956 ± 0.0007 0.482 ± 0.006

0.163 ±0.002 0.000 0.596 ± 0.003

exposed to a toxicant for a short period of time (24-96 hours). Given the
generic reaction between a bivalent metal cation and a biotic ligand,

=BL" + M 2+ = =BLM+

and the model equilibrium constant in Eq. 9.22, show that EC50 for a
toxic bivalent metal cation (e.g., Cd 2+ ) should increase linearly with the

242 The Chemistry of Soils

concentration of a nontoxic bivalent metal cation (e.g., Ca + ) that can
also bind to the biotic ligand.

10. The concentration of Cu 2+ causing 50% immobilization of the freshwater
test organism Daphnia magna (water flea), after 48 hours of exposure
(EC50) is observed to increase with the concentration of Ca + according
to the linear regression equation

EC 50 = 9.97 + 25.0 c Ca

where EC50 is in nanomoles per liter and cc a is in moles per cubic meter.
Separate experiments show that EC50 is associated with a=BLCu = 0.47.
Calculate a value of the Vanselow selectivity coefficient for Cu — > Ca
exchange on the biotic ligand of D. magna. Explain why EC50 increases as
the concentration of Ca + increases.

*11. The presence of a complexing ligand that can bind a toxic metal cation
in competition with a biotic ligand should reduce the concentration of
the free metal cation and thereby inhibit toxic effect. For example, the 48-
hour LC50 for Ag toxicity to D. magna increases from 0.47 |xg Ag L to
1.2 |xg Ag L _1 when the concentration of chloride ions is increased from
0.05 to 1.0 mM. (These LC50 values are expressed in terms of the total
soluble Ag concentration that induces acute toxicity.) Given the value of
the equilibrium constant for the formation of the soluble complex AgCl ,

Ag+ + CI" = AgCl K s = io 3 - 31

determine whether this increase in LC50 with chloride concentration is
reasonable.

12. The concentration of Ni 2+ causing a 50% reduction in normal barley root
elongation (EC50) is a linear function of the concentrations of protons,
Ca , and Mg + in the soil solution. Given the parameter values

logK cNi BL = 3.60 ± 0.53, logK c HBL = 4.52 ± 0.62,
logKcCaBL = 1-50, logK cMg BL = 3.81 ± 0.60

estimate EC 50 at pH 5.7 if [Ca 2+ ] = 2 x 10" 3 mol L" 1 and [Mg 2+ ] = 2.5
x 10 -4 mol L _1 . Take a=BLNi = 0.05.

13. The concentration of Cu 2+ causing 50% immobilization of D. magna
after 48 hours (Problem 11) is affected by H + , Na + , Ca 2+ , and Mg 2+ as
competing cations. Given the parameter values

logKcCuBL = 8.02, logK c HBL = 5.40, logK cNa BL = 3.19,

logK c caBL = 3.47, logKcMgBL = 3.58

calculate EC50 for pH ranging between 6.0 and 8.5 in a natural water
having [Na+] = 0.002 mol L _1 , [Ca 2+ ] = 0.003 mol L _1 , and [Mg 2+ ]

Exchangeable Ions 243

= 0.0006 mol L . Does increasing pH increase or decrease the acute
toxicity of Cu + to D. magna?

14. Benedetti et al. [Benedetti, M. R, W. H. van Riemsdijk, and L. K. Koopal.
(1996) Humic substances considered as a heterogeneous Donnan gel
phase. Environ. Sci. Technol. 30:1805.] explain the origin of Eq. 9.28 in
terms of the Donnan model, in which ions are distributed between a
slurry containing charged particles and a supernatant solution (Section
8.1) according to the average properties of a diffuse-ion swarm. (Their
Eq. 1 is the same as Eq. 9.28, with the correspondences Q ■<=>• a p and v>d •O-
V ex .) Experimental measurements of V ex as a function of ionic strength
are summarized in their Table 2 and their Figure 4 for humic and fulvic
acids.

a. Use linear regression analysis to estimate the parameter a and the
coefficient of log I in Eq. 9.29 for the data on V ex in Table 2 of the
article by Benedetti et al. Be sure to include 95% confidence limits
with your results.

b. Typical values of the specific surface area for humic substances range
from 500 to 800 m 2 g _1 . Use the model equation for V ex in Problem 9
of Chapter 8 to estimate the value of the parameter a in Eq. 9.28
based on this range of as values.

15. The table presented here lists value of log Km an d Pm (Eq- 9.30) for
bivalent metal (M) cation complexation by carboxyl groups in humic
acids. Discuss the values of the product Pm log Km in terms of concepts
presented in sections 8.3 and 9.3.

Cation log K^

Ca
Cd
Co
Cu

Hg
Mg

-1.1

0.90

-1.37

0.78

-0.20

0.73

-0.24

0.79

2.23

0.56

5.2

0.32

-0.6

0.77

-0.3

0.72

-0.26

0.64

1.25

0.60

-1.36

0.78

0.11

0.67

Colloidal Phenomena

10.1 Colloidal Suspensions

Colloids in soils are solid particles of low water solubility with a diameter that
ranges between 0.01 and 10 |xm (i.e., clay-size to fine-silt-size particles). The
chemical composition of these particles may vary from that of a clay mineral
or metal oxide to that of soil humus, or, more broadly, maybe a heterogeneous
combination of inorganic and organic materials. Regardless of composition,
the characteristic property of colloids is that they do not dissolve readily in
water to form solutions, but instead remain as identifiable solid particles in
aqueous suspensions.

Colloidal suspensions are said to be stable (and the particles in them
dispersed) if no measurable settling of the particles occurs over short time
periods (e.g., 2—24 hours). Stable suspensions of soil colloids lead to erosion
and illuviation because the particles entrained by flowing water or percolating
soil solution remain mobile. Stable suspensions also have a secondary effect
on the mobility of inorganic and organic adsorptives, especially radionuclides,
phosphate, or pesticides, that can become strongly bound to soil colloids. Thus,
colloidal stability is connected closely with particle and chemical transport.

Soil particles with a diameter that falls into the middle of the colloidal
range, from approximately 100 nm to l|xm, are those observed to remain
suspended in surface or subsurface waters for long periods of time. Colloids
with a diameter that is less than this range coalesce and grow rather quickly
to form larger particles, whereas colloids with a size that is larger than the
midrange appear to settle rather quickly under the influence of gravity, at least

244

Colloidal Phenomena 245

in quiescent suspensions. Because of these observations, the study of soil
colloidal phenomena has tended to focus on the behavior of midrange par-
ticles, including the influence of their surface chemistry, with the goal of
pinpointing conditions that either ensure continued suspension or promote
particle growth.

The process by which soil colloids in suspension coalesce to form
bulky porous masses is termed flocculation. The particles formed during
flocculation — also termed coagulation — and removed from suspension by set-
tling are themselves candidates for further transformation into aggregates, the
organized solid masses that figure in the structure, permeability, and fertil-
ity of soils. Flocculation processes are complicated phenomena because of
the varieties of particle morphology and chemical reactions they encompass.
From the perspective of kinetics, perhaps the most important generalization
that can be made is the distinction between transport-controlled and surface
reaction-controlled flocculation, parallel to the classification of adsorption pro-
cesses described in Special Topic 3 (Chapter 3). Flocculation kinetics are said
to exhibit transport control if the rate-limiting step is the movement of two or
more particles toward one another prior to their close encounter and immedi-
ate coalescence to form a larger particle. Surface reaction control occurs if it is
the particle coalescence process instead of particle movement toward collision
that limits the rate of flocculation.

Three models of the transport-control mechanism for flocculation are
in common use to interpret the kinetics of particle formation in colloidal
suspensions (Fig. 10.1). The best known of these models is Brownian motion
(perikinetic flocculation), which applies to quiescent suspensions of diffusing
particles with a diameter that lies in the lower to middle portion of the col-
loidal range (< l|xm). Flocculation caused by stirring a colloidal suspension
is described as shear induced (orthokinetic flocculation), whereas that caused
by the settling of particles under gravitational or centrifugal force is described
as differential sedimentation. In all three kinetics models, a second-order rate
coefficient (Table 4.2) appears that is equal to the product of an effective
cross-sectional area for two-particle collisions (a geometric factor) times an
effective two-particle relative velocity (a kinematic factor). Large rate coeffi-
cients for flocculation thus are produced by optimal combinations of particle
size (geometry) and opposing particle velocities (kinematics).

In a quiescent soil suspension, the motions of the particles are incessant
and chaotic because of the thermal energy the particles possess. As shown
by Albert Einstein in his doctoral dissertation, these Brownian motions in
suspension are analogous to the diffusive motions of molecules in solution,
with a diffusion coefficient expressed by the Stokes-Einstein model:

D = k B T/6^T)R (10.1)

InEq. 10.1, kg is the Boltzmann constant (see the Appendix), r\ is the shear vis-
cosity of water, and R is the radius of the colloidal particle (assumed effectively

246 The Chemistry of Soils

'-y ^

Perikinetic

Differential Sedimentation

Mechanisms of transport-
controlled coalescence
in colloidal suspensions

Orthokinetic

Figure 10.1. Three mechanisms of flocculation lead to rapid coalescence. Perikinetic
flocculation usually is engaged in by colloids smaller than 1 |xm, whereas the other two
mechanisms apply mainly to colloids larger than 1 u.m.

spherical). The Stokes-Einstein relation indicates that a colloid will diffuse
more rapidly if the temperature is high, if the fluid viscosity is low, or if the
colloid is very small. Perikinetic flocculation postulates Brownian motion of
colloidal particles that leads them to collide by chance, after which they coalesce
instantaneously to form a dimer. The second-order rate coefficient describing
this process is

23tRiiDh

(10.2)

where Rn is the radius of the dimer and Dn is the diffusion coefficient of
one of the colliding monomers relative to that of the other, as depicted from
a reference point taken as their center of mass. In a first approximation, Rn
is just twice the monomer radius, and Dn is just twice the monomer diffu-
sion coefficient as modeled by Eq. 10.1. With these simplifications, the rate
coefficient for dimer formation becomes

,SE

87rRD SE = K SE

(10.3)

Colloidal Phenomena 247

where

K SE = 4k B T/3T) (10.4)

is a constant parameter equal to 6.16 x 10 -18 m 3 s _1 at 25 °C if water is
the suspending fluid. Note that the use of the Stokes-Einstein relation leads
to an exact cancellation of the monomer radius R from the perikinetic rate
coefficient.

Orthokinetic flocculation postulates the capture of a monomer in the
streamlines around another monomer while the former attempts to pass the
latter (Fig. 10.1). This mechanism requires a fluid velocity gradient (or shear
rate), G, that permits one monomer to overtake the other while they both are
being convected by the fluid. The rate coefficient for orthokinetic aggregation
is thus the product of the effective cross-sectional area of a dimer (proportional
to the volume of a capture sphere enclosing the overtaken monomer and having
a radius equal to that of the dimer formed) times the relative velocity of the
overtaking monomer:

k = -R 3 jG (10.5)

Usually, Rn is approximated once again by twice the monomer radius, such
that

16 ,
k D = — GR 3 (10.6)

is the model rate coefficient for shear-induced flocculation. In this case, the
geometric factor increases strongly with particle size. Typical values for G
are in the range 1 to 10 s _1 for flowing natural waters. The importance of
orthokinetic flocculation as the monomer radius increases can be seen by
forming the dimensionless ratio of the right sides of Eqs. 10.3 and 10.6:

K«f perikinetic rate 1.16

— - = — : : = (10.7)

k D orthokinetic rate GR 3

where R is in units of micrometers and G is in units of inverse seconds.
Orthokinetic flocculation rates exceed those of perikinetic flocculation when-
ever R > G -1 ' 3 numerically (i.e., for monomers in the mid- to upper range of
colloidal diameters, given the typical values of G).

Transport control of flocculation by differential sedimentation in a gravi-
tational field is modeled by applying the well-known Stokes law for the terminal
velocity of a particle settling in a viscous fluid to each particle in a pair of
monomers with different radii, then multiplying the resulting difference in
velocity of the two particles by the cross-sectional area of the dimer they form
on collision:

k D s= -f (p s -Pf)^R? 2 |Ri2-R2| (10-8)

248 The Chemistry of Soils

where g is the gravitational acceleration, and p s and pf are mass densities of
the monomers and the fluid in which they are settling respectively. In this case,
one monomer ( 1 ) overtakes the other (2) because it is larger and, therefore, has
a larger terminal velocity. The dimer radius R12 may again be approximated
by the sum of the monomer radii. Given the fourth-power dependence on
monomer size and the typical magnitude of the constant prefactor in Eq.
10.8 (about 6 x 10 6 m _1 ), one deduces that the differential sedimentation
mechanism only becomes important for particles larger than about l|xm.

For colloidal particles smaller than lixm, the timescale for flocculation in
a quiescent suspension can be estimated with the perikinetic rate coefficient in
Eq. 10.3. According to Table 4.2, the half- life for flocculation is then the inverse
of the product of the rate coefficient and an appropriate initial concentration
of colloids. The rate at which the total number of particles per cubic meter of
suspension, p, decreases because of a flocculation process can be described by
the rate law:

-p = -K SE p 2 (10.9)

a special case of Eq. 4.5 with b = 2. Equation 10.9, known as the von Smolu-
chowski rate law, contains the square of the number density p on the right
side because two particles are involved in a collision, so the rate of flocculation
depends on the number density of each. The corresponding half-life is

ti/2 = 1/KsePo = 1-62 x 10 17 /po (10.10)

where ti/2 is in s and p is the initial number density. For example, if a
suspension contains initially 10 14 colloidal particles per cubic meter, it follows
from Eq. 10.10 that ti/2 ~ 1600 s for the flocculation of these particles.

10.2 Soil Colloids

Colloids suspended in soil solutions will exhibit shapes and sizes that reflect
both chemical composition and the effects of weathering processes. Kaolinite
particles, for example, are seen in electron micrographs as roughly hexagonal
plates comprising perhaps 50 unit layers (each layer is a wafer the thickness
of a unit cell, about 0.7 nm), which are stacked irregularly and interconnected
through hydrogen bonding between the OH groups of the octahedral sheet
and the oxygens of the tetrahedral sheet (Section 2.3). In the soil environment,
weathering produces rounding of the corners of kaolinite hexagons and coats
them with iron oxyhydroxides and humus. Fracturing of the plates also is
apparent along with a "stair-step" topography caused by the stacking of unit
layers having different lateral dimensions. These heterogeneous features lead to
flocculation products (floccules) that are not well organized. The fabric of the
floccules consists of many stair-stepped clusters of stacked plates, interspersed

Colloidal Phenomena 249

with plates in edge— face contact (possibly because of differing surface charges
on edges and faces) that are arranged in a porous three-dimensional network.

Similar observations have been made for 2: 1 clay minerals. Illite, for exam-
ple, is seen in electron micrographs as platelike particles stacked irregularly,
although the bonding mechanism causing the stacking is an inner-sphere sur-
face complex of K + , not hydrogen bonding. These particles also exhibit a
stair-step surface topography and frayed edges produced by weathering. Coat-
ings of Al-hydroxy polymers and humus may have formed, with these features
being made even more heterogeneous by a nonuniform distribution of iso-
morphic substitutions, with regions of layer charge approaching 2.0 grading
to regions of layer charge near 0.5 (Section 2.3). These characteristics and
a slight flexibility of the illite plates (probably caused by strains associated
with isomorphic substitution) lead to floccules that are like those for kaolinite
particles, but with greater porosity.

Smectite and vermiculite have a lesser tendency to form colloids com-
prising extensive stacks because their layer charge is smaller than that of illite
and, therefore, is less conducive to inner-sphere surface complexation. They
are also more flexible, probably because of stresses induced by their more
extensive isomorphic substitutions in the octahedral sheet. Floccule struc-
tures built of these colloids exhibit irregularly shaped plates organized in a
random framework of high porosity. Surface heterogeneities brought on by
nonuniform layer charge and the sorption of Al-hydroxy polymers or humus
add to the heterogeneity. Floccules of 2:1 clay minerals subjected to drying and
rewetting cycles can form aggregates comprising regularly stacked layers. This
parallel alignment of unit layers can be observed in very thick suspensions
of Na-smectite and in any suspension of bivalent cation-saturated smectite.
Stacked layers of Na-smectite are important in arid-zone soils because their
ordered structure prevents the development of the large pores essential to soil
permeability. They are created by the dewatering of suspensions originally
containing dispersed unit layers (i.e., initially stable suspensions). Stacked lay-
ers of Ca-smectite (or any bivalent cation-saturated smectite) are organized by
outer-sphere surface complexes of Ca + with pairs of opposing siloxane cavi-
ties. The octahedral salvation complex Ca(H20) 6 is arranged in the interlayer
region with its principal symmetry axis perpendicular to the siloxane surface.
Four of the solvating water molecules lie in a central plane parallel to the
opposing siloxane surfaces, whereas the remaining two water molecules reside
in planes between the siloxane surfaces and the central plane to give an inter-
layer spacing of 1.91 nm (Fig. 10.2). An outer-sphere surface complex of this
kind is a characteristic structure in suspensions of smectite bearing bivalent
exchangeable cations.

Therefore, in relatively dilute, stable suspensions, Na-montmorillonite
colloids will have a different structure from Ca-montmorillonite colloids.
In stable suspensions of montmorillonite colloids bearing both Na + and
Ca 2+ , one would expect a continuous transition from stacked-layer particles
to more or less single-layer particles as the charge fraction of exchangeable

250 The Chemistry of Soils

O 6><

Figure 10.2. The outer-sphere surface complex between Ca 2 + and opposing silox-
ane surfaces bounding the interlayer region in the three-layer hydrate of Ca-
montmorillonite that occurs in aqueous suspensions.

Na + increases. Sharp increases in the number of single-layer particles are
indeed observed when the charge fraction of Na + on the clay increases
from 0.15 to 0.30, if the electrolyte concentration is low, indicating that the
Ca-montmorillonite colloids are being broken up in favor of more or less
single-layer particles. On the other hand, when ENa < 0.3, these latter colloids
are the favored entities, with any residual exchangeable Na + relegated to their
external surfaces.

Heterogeneous soil colloids tend to harbor a variety of complex, irregular
particles, including microbes, that are linked by tendrils of extracellular organic
matter and cell wall compounds (Fig. 10.3). These colloids tend to coalesce
rather slowly, unless the ionic strength is high, to form relatively compact
floccules. Inorganic particles also can associate with smaller organic colloids
by coalescence, with the latter particles possibly changing their conformation
as a result of interactions with the charged surface of the inorganic partner. If
the organic colloids are larger than the inorganic particles, or if they emanate
long tendrils, the organic colloids may bind the smaller inorganic particles
into a fibrous network of whorls with a complex overall morphology. These
larger particles, in turn, may settle quickly.

10.3 Interparticle Forces

Regardless of how complex a soil colloid may be, it still is subject to the forces
brought on by its fundamental properties of mass and charge. The property
of mass gives rise to the gravitational force and the van der Waals force. The
property of charge gives rise to the electrostatic force. The first two forces cause
a colloidal suspension to be unstable, whereas the second can cause it to remain

Colloidal Phenomena 251

U°

/ i

Small organic colloid

<^j Inorganic particle

Organic tendril

Figure 10.3. Formation and structure of heterogeneous natural colloids comprising
small, roughly spherical particles, including microbes, and organic tendrils. Scheme
after Buffle, J. et al. (1998) A generalized description of aquatic colloidal interactions.
Environ. Sci. Technol. 32:2887-2899.

stable. The gravitational force (corrected for the effect of buoyancy) initiates
and sustains particle settling. This force is created simply by the gravity field
of the earth. The other two forces are properly interparticle forces: They act
between colloids either to attract them or to repel them.

The colloids in a stable soil suspension can be envisioned, at least in an
ideal geometric sense, to be roughly spherical (humus and metal oxides) or to
comprise one or more unit layers stacked together (clay minerals). If spherical
colloids are large relative to the thickness of their diffuse swarm of adsorbed
ions or, in the case of clay minerals, if layer stacking is not extensive or highly
irregular, one can imagine the forces the particles exert on one another as

252 The Chemistry of Soils

coming from interacting planar surfaces. Interparticle forces can be discussed
in detail on the basis of this geometric simplification.

The van der Waals interaction between soil colloids is exactly analogous to
that between soil humus and organic polymers or clay minerals (sections 3.4
and 3.5). Over a time interval that is much longer than 10 s,the distribution
of electronic charge in a nonpolar molecule is spherical. However, on a
timescale < 10 -16 s (approximately the period of an ultraviolet light wave),
the charge distribution of a nonpolar molecule will exhibit significant devia-
tions from spherical symmetry, taking on a flickering, dipolar character. These
deviations fluctuate rapidly enough to average to zero when observed over, say,
10 -14 s (the period of an infrared light wave), but they persist long enough to
attract or repel and, therefore, induce distortions in the charge distributions of
neighboring molecules. If two nonpolar molecules are brought close together,
each will induce in the other a fluctuating dipolar character and the correla-
tions between these induced dipole charge distributions will not average to
zero, even though the individual dipole distributions themselves will average
to zero. The correlations between the two instantaneous dipole moments pro-
duces an attractive interaction with a potential energy that is proportional to
the inverse sixth power of the distance of separation. The resulting attractive
force is known as the van der Waals dispersion force. At small values of the
separation distance, this interaction can be strong enough to cause particles
to coalesce.

Suppose that a nonpolar molecule confronts the planar surface of a solid.
The van der Waals dispersion energy for the attractive interaction between
the single molecule and the planar solid surface can be shown to vary as the
inverse third power of their distance apart. The inverse power is smaller than
six because of the additive effect of van der Waals forces between the many
atoms of the solid and the nonpolar molecule. Now suppose that, instead of
a single nonpolar molecule, a solid surface comprising nonpolar molecules
confronts the planar surface. A calculation of the van der Waals energy per
unit area of surface then gives the equation

van der Waals energy = (10.11)

\2nd l

where d is the distance separating the planar solid surfaces and A is called the
Hamaker constant. Equation 10.11 shows that the van der Waals dispersion
energy (per unit area) falls off as the inverse square of the distance separating
two opposing planar surfaces. Because it is additive for the many molecules in
the two solids, this attractive interaction (hence the negative sign in Eq. 10.11)
decreases with distance of separation much more slowly than the interaction
between an isolated pair of molecules. The Hamaker constant, which gives
a measure of the magnitude of the van der Waals energy at any separation
distance, has a value near 2 x 10 } for soil colloids.

The van der Waals interaction is the cause of particle coalescence after
a collision induced by Brownian motion, stirring, or settling, as described in

Colloidal Phenomena 253

Section 10.1. If the particles each bear a net charge, however, their tendency to
collide and stick together is strongly affected by an electrostatic force between
them. A repulsive force arises if the sign of the charge on each particle is the
same; otherwise, an attractive force arises that adds to the van der Waals attrac-
tion in promoting coalescence. The repulsive electrostatic interaction can be
shown to be proportional to the product of three factors: the exclusion vol-
ume (Problem 9 in Chapter 8; see also sections 8.4 and 9.5), the bulk aqueous
solution concentration of ions that screen the particle charge (Section 7.2),
and an exponentially decreasing function of d. Expressed per unit area of
particle surface and in the notation of the model equation for V ex that was
applied to monovalent ions in a diffuse swarm in Problem 9 of Chapter 8 and
in Section 9.5,

c
electrostatic repulsion energy oc — exp (— Kd) (10.12)

where

k = (fic ) l i2 = (2F 2 c /e DRT) 1 /2 (10.13)

is a diffuse-swarm screening parameter with an inverse that has the dimen-
sions of length. In Eq. 10.13, F is the Faraday constant, £ is the permittivity
of vacuum (see the Appendix), D is the dielectric constant of water (78.3 at
25 °C), R is the molar gas constant (as in Problem 9 of Chapter 1), and T is
absolute temperature. The parameter k determines both the spatial extent of
V ex [the average volume of aqueous solution that encompasses the (monova-
lent) ions in the diffuse swarm that screen the particle charge (Section 9.5)]
and the spatial decay of the electrostatic repulsion energy as epitomized in the
exponential factor appearing in Eq. 10.13. The value of k -1 at 25 °C ranges
from 1 to 30 nm as c ranges from 0.1 to 100 mol m , which is typical of soil
solutions. Thus, nanometer length scales characterize the region around charged
colloids in which the screening of particle charge by electrolyte ions is effective.

As c is increased, it follows from eqs. 10.12 and 10.13 that the electro-
static repulsion between charged colloids will drop off ever more rapidly near
the colloids, allowing them to approach more closely until they come under
the dominating influence of the attractive van der Waals energy and coalesce.
The smallest concentration of electrolyte, in moles per cubic meter, at which a
soil colloidal suspension becomes unstable and begins to undergo perikinetic
flocculation is called the critical coagulation concentration (ccc). The value of
the ccc will, in general, depend on the nature of the participating colloids, the
composition of the aqueous solution in which they are suspended, and the
time allowed for settling. A simple laboratory measurement of the ccc entails
the preparation of dilute (< 3 kg m -3 solids concentration) suspensions in a
series of electrolyte solutions of increasing concentration. After about 1 hour
of shaking and a subsequent standing period of 2 to 24 hours, the suspensions
that have become unstable will show a clear boundary separating the settled
solid mass from an aqueous solution phase, and the ccc can be bracketed

254 The Chemistry of Soils

between two values determined by the largest electrolyte concentration at
which apparent flocculation did not occur and the smallest at which it did.

The study of soil colloidal stability has not yet produced exact mechanistic
theories, but nonetheless, general relationships between stability, interparticle
forces, and surface chemistry have been developed that are of predictive value.
One of these relationships is the Schulze-Hardy Rule. This empirical generality
concerning the ccc, first suggested by H. Schulze and generalized by W. B. Hardy
more than a century ago, can be stated as follows:

The critical coagulation concentration for a colloid suspended in an
aqueous electrolyte solution is determined by the ions with charge oppo-
site in sign to that on the colloid (counterions) and is proportional to an
inverse power of the valence of the ions.

Published studies indicate that ccc values for monovalent counterions generally
lie in the relatively narrow range of 5 to 100 mol m -3 , whereas those for bivalent
counterions typically lie in the range of 0.1 to 2.0 mol m , if the coalescing
particles are inorganic, or largely so. This order-of-magnitude difference in
ccc between monovalent and bivalent ions illustrates the Schulze-Hardy Rule
qualitatively.

The relationship between ccc and counterion valence can be interpreted
quantitatively on the basis of a simple consideration of length scales in the
diffuse-ion swarm. Adsorption of counterions in the diffuse swarm acts to
screen particle charge, in that the range of the electrostatic repulsion energy
created by a charged particle is diminished by this adsorption. It is reason-
able to assign to each counterion of charge Ze [e = pro tonic charge = F/Na,
where Na is the Avogadro constant (see the Appendix)], a surface patch of
equal and opposite charge that it screens. If this screening is to be effec-
tive, the coulomb potential energy restricting the counterion to the vicinity of
the charged surface patch should be of the same order of magnitude in abso-
lute value as the thermal kinetic energy of the counterion, jkfiT, where k% is
the Boltzmann constant (as in Eq. 10.1) and T is absolute temperature:

IZj ° • -k B T (10.14)

47T£ DLs 2

The parameter L s characterizes a thermal screening length with a magnitude
that depends only on physical variables. Equation 10.14 can be rewritten in
terms of the diffuse-swarm parameter |3 introduced in Problem 9 of Chapter 8
and defined in Eq. 10.13:

L s R» Z 2 (P/4ttN a ) (10.15)

At 25 °C, P/47tNa = 1.43 nm, once again demonstrating that nanometer
length scales are relevant to charge screening.

Effective charge screening by a counterion in the diffuse swarm must mean
that the screening length for the electrostatic repulsion energy (Eq. 10.12) is

Colloidal Phenomena 255

comparable with L s in Eq. 10.15. Otherwise, the influence of particle charge
would "leak out" beyond the region of bound counterions. The screening
length is, of course, k , where now we set k = Z (/8c ) 2, with the valence of
the screening counterion added to the definition given in Eq. 10.13. Therefore,
effective screening requires the constraint

kLks 1 (10.16)

from which an equation for the ccc can be derived by introducing Eq. 10.15
and the revised definition of k:

ccc ^ (167T 2 N 2 A /^ 3 ) Z~ 6 (10.17)

The prefactor in Eq. 10.17 is equal to 45 mol m at 25 °C. Given the typical
range of ccc values for monovalent counterions (5-100 mol m -3 ), the estimate
of ccc provided by Eq. 10.17 for Z = 1 is reasonable. For bivalent counterions,
the corresponding estimate of ccc is 0.7 mol m -3 , which also lies within the
range of typical values: 0.1 to 2 mol m . Equation 10.17 is a quantitative
expression of the Schulze-Hardy Rule, which reveals it to be a manifestation
of effective charge screening — a condition induced by decreasing the range
of the electrostatic repulsion energy generated by a charged colloid until it is
small enough to make the resultant coulomb attraction of a counterion toward
the particle strong enough to quench the thermal kinetic energy that otherwise
would send the counterion wandering off.

10.4 The Stability Ratio

Models of the second-order rate coefficient for transport-controlled floc-
culation, presented in Section 10.1 (eqs. 10.3, 10.6, and 10.8), show only a
dependence on physical parameters, such as absolute temperature, fluid prop-
erties, and colloid size. These models evidently do not depend on chemical
variables, such as background electrolyte concentration or pH, even though
these latter variables must affect the flocculation of soil colloids, as the very
definition of ccc plainly demonstrates. Under conditions in which rapid periki-
netic flocculation is occurring, direct measurements of the rate of flocculation
lead to k p values in the range 1 to 4 x 10 m s at 25 °C for suspen-
sions of synthetic mineral or organic colloids. This range of values is close to,
but systematically smaller than k = 6.2 x 10 -18 m 3 s _1 , as obtained from
Eq. 10.4 applied at 25°C. Thus the Stokes-Einstein model of flocculation is
generally consistent with observations of rapid perikinetic flocculation. The
residual discrepancy between theory and experiment can be explained quan-
titatively in terms of the detailed mechanics of dimer formation: The dimer
radius Rn is less than twice the monomer radius, and the relative diffusion
coefficient Dn is less than twice the monomer diffusion coefficient, because
of fluid mechanical effects that occur when two monomers are brought close

256 The Chemistry of Soils

together. These effects suffice to reduce k p in Eq. 10.2 by the required factor
of two to five relative to k_ in Eq. 10.3.

Rapid perikinetic flocculation occurs at the ccc, and it is under this con-
dition that Eq. 10.3 provides a useful model of the rate coefficient to be
introduced into the von Smoluchowski rate law (Eq. 10.9). If the concen-
tration of flocculating electrolyte is smaller than the ccc, the value of the
second-order rate coefficient for flocculation also is found to be smaller (as
would be expected from consideration of the method for measuring the
ccc described in Section 10.3). Figure 10.4 shows the change in the ratio
k([KCl] = 80 mmol kg )/k caused by an increase in electrolyte concen-
tration for synthetic hematite colloids suspended in KCl solution at pH 6 and
25 °C. No change in the rate coefficient k for flocculation was observed at
KCl concentrations above 80 mmol kg ; hence, all rate coefficients were nor-
malized to this molal concentration. The ratio k([KCl] = 80 mmol kg )/k
displays a gradual decline toward unit value as [KCl] is increased by more
than an order of magnitude. To the extent that KCl behaves as an indifferent
electrolyte (see Sections 7.4 and 9.1) in respect to hematite, this decline can be
interpreted as an effect of electrolyte concentration on the diffuse-ion swarm,
particularly for Cl _ , which should be the screening ion, given the positive
surface charge on hematite expected at pH 6 (Section 7.4). Corresponding
to the increase of concentration in Figure 10.3 there is a decrease by a factor
of three in the screening length scale k -1 (Eq. 10.13). This weakening of the

10 -

Hematite
pH6

ccc

—\ —

— i —

h — i^i

- T J

• i

■ — 1 '

20 40 60 80

[KCl] (mmol kg" 1 )

100

Figure 10.4. Dependence of the second-order rate coefficient for the coalescence of
hematite colloids suspended in KCl solution at pH 6(<7p > 0) on KCl concentration.
The value of the critical coagulation concentration (ccc) for the suspension is indicated
by the arrow. Data from Cho rover, J., J. Zhang, M.K. Amistadi, and J. Buffle (1997)
Comparison of hematite coagulation by charge screening and phosphate adsorption.
Clays Clay Miner. 45: 690-708.

Colloidal Phenomena 257

electrostatic repulsion energy (Eq. 10.12) near a hematite colloid is sufficient
to provoke an increase in the rate coefficient for particle coalescence by an
order of magnitude. Thus, Figure 10.4 is a graphic portrayal of the transi-
tion from surface reaction control to transport control in the flocculation of
hematite colloids.

The quantity plotted against concentration in Figure 10.4 is termed the
stability ratio:

initial rate of rapid flocculation

W=^— rn Y - , (10.18)

initial rate of flocculation observed

where rate is interpreted as in Eq. 10.9 with p set equal to p D . Given Eq.
10.10, W is also the ratio of a characteristic timescale for coalescence observed
under prescribed conditions to that observed under conditions producing
rapid flocculation. These latter conditions are associated with the value of
a chemical variable, the electrolyte concentration, leading to an alternative
definition of ccc:

lim W= 1 (10.19)

c^ccc

where c is the concentration of the counterion in an indifferent electrolyte.

Charge screening that induces rapid flocculation is the result of weak
interactions between a diffuse swarm of adsorptive counterions and a charged
particle surface (Section 10.3). Attractive van der Waals interactions, which are
always present, then act to cause coalescence of the colloids. The mechanism
by which rapid flocculation is brought on is not unique, however, because the
repulsive coulomb interaction between two colloids having the same charge
sign also can be weakened by charge neutralization. This mode of inducing
rapid flocculation is the result of strong interactions between adsorptive coun-
terions and a charged particle surface [i.e., those typically associated with
specific adsorption processes (see Section 7.2 and Chapter 8)]. These include
protonation and the inner-sphere surface complexation of metal cations or
inorganic/organic anions.

Figure 10.5 illustrates the effect of pH on the second-order rate coefficient
k for synthetic hematite colloids suspended in NaNC>3 solution at 25 °C. Rapid
coalescence was observed at any pH value when [NaCl] = 100 mol m -3 , the
value of k being 1.8 x 10 m s , which is close to that predicted by Eq. 10.4.
At lower [NaCl], an effect of pH is apparent, with the value of k decreasing by
up to three orders of magnitude as pH is varied below or above approximately
9.2. The graph in Figure 10.5 is essentially a plot of — log W versus pH, because
logk= — logW + logk([NaN0 3 ] = 0.1M) according to the definition of W
in Eq. 10.18. The value of pH required to produce a maximum value of k and,
therefore, W = 1.0 is termed the point of zero charge (p.z.c):

lim log W = (10.20)

pH^- p.z.c.

258 The Chemistry of Soils

5.0
0.5

E. 0.05

O
X

0.005
0.0005

0.010 M

Hematite

0.001 M NaNO,

Figure 10.5. Dependence of the second-order rate coefficient for the coalescence of
hematite colloids suspended in NaCl solution on pH at three electrolyte concentrations.
The value of the ccc for the suspension is indicated by a horizontal solid line. Data from
Schudel, M. et al. Absolute aggregation rate constants of hematite particles in aqueous
suspensions. /. Colloid Interface Sci. 196:241-253.

Direct measurement of p.z.c. (as p.z.s.e.) indicated that p.z.c. ~ 9.2
(Section 7.4). To the extent that the condition er p = is represented by Eq.
10.20, the terminology it introduces and that introduced in Section 7.4 are
mutually consistent. Note that charge screening by the diffuse-ion swarm is
not possible when pH = p.z.c. (see Eq. 7.5).

Unlike the behavior of W in response to increases in the concentration
of an indifferent electrolyte (Fig. 10.4), W typically exhibits two branches as
pH is increased from below to above the p.z.c. The "hairpin" — log W ver-
sus pH plot in Figure 10.5 broadens considerably as the concentration of the
electrolyte is increased. This straightening-out effect can be understood as a
synergism between pH and [NaNC^] taken as controlling chemical variables.
The "hairpin" is bent out into a straight horizontal line as [NaNC>3 ] approaches
the ccc because charge screening is contributing more and more to the pro-
duction of rapid flocculation at any pH value. The asymmetry of the hairpin
about the p.z.c. signals the existence of physical factors controlling W instead
of electrolyte concentration and pH (e.g., particle surface and morphological
heterogeneities). The fact that there is a hairpin at all in Figure 10.5 derives
from the change of er p from positive to negative as pH is increased and passes
through the p.z.c. Coulomb repulsion will promote surface reaction control of

Colloidal Phenomena 259

flocculation irrespective of the sign of a p . Note that anions become the counter-
ions causing flocculation at pH < p.z.c, whereas cations become the counterions
atpH> p.z.c.

Figure 10.6 shows the effect of the strongly adsorbing anion, H2PO7/, on
the stability ratio of synthetic hematite colloids suspended in 1 mol m KCl
solution at pH 6 at 25 °C. The plot of log W versus log [F^PO^] displays
a characteristic "inverted hairpin" shape that signals particle charge reversal
when log [H2PO4] ~ —4.5, under the experimental conditions selected (p ~
2.610 16 m -3 ). This value of log [H2PO4] is termed the p.z.c. with respect to
H 2 P07:

lim logW=0

log[]-> P-z-c.

(10.21)

Note that p.z.c. with respect to a strongly adsorbing ion is a negative quantity,
whereas p.z.c. with respect to protons is a positive quantity. Thus p.z.c. with
respect to H2PO4 is —4.5.

Figure 10.7 illustrates the effect of the strongly adsorbing organic anions
CH3(CH2) n COO - (n = 2, 7, 9, 11) on the stability ratio for synthetic hematite
colloids suspended in 50 mol m -3 NaCl at pH 5.2. The log-log plots indicate
p.z.c. values in the range —5 to —3, and their inverted hairpin shape exhibits
asymmetry about the p.z.c. similar to what is apparent in Figure 10.6. The p.z.c.
value decreases as the number of C atoms in the anion increases, suggesting
that hydrophobic interactions may play a role in promoting rapid flocculation.

1(T-

•-\

10 3 -

•/

•*

• /

.•

\ i

• /

W 1() 2,

•

p.z.c.

/•

10 1 1

Hematite

• /

pH6

•

1 mM KCl

' 1

10°-

1 ,—

— p-

— i —

*>^ — *

r ' 1 —

-7 -6 -5 -4 -3

log[H 2 P0 4 -]([]inmolL- 1 )

Figure 10.6. Dependence of the stability ratio for hematite colloids suspended in
1 mM KCL at pH 6 on the concentration of F^PO^ added to the suspension to induce
flocculation. The value of the point of zero charge (p.z.c.) with respect to H2P0 4 is
indicated by the arrow. Data from Chorover, J. op. cit.

260 The Chemistry of Soils

2.0

1.5

1.0

0.5

0.0

Hematite

pH 5.2

50 mM NaCI

_l_

-7.0 -6.0 -5.0 -5.0 -3.0 -2.0
log [CH 3 (CH 2 ) n COO ]([ ] in mol L 1 )

Figure 10.7. Dependence of the stability ratio for hematite colloids suspended
in 50 mM NaCI at pH 5.2 on the concentration of aliphatic acid anions
[CH3(CH2)„COO~, n = 2, propionate; n = 7, caprylate; n = 9, caprate; n = 11,
laurate] added to the suspension to induce flocculation. The minimum in each plot
indicates the p.z.c. with respect to a given aliphatic anion. Note that rapid flocculation
occurs at a NaCI concentration smaller than 100 mM, the nominal ccc. Data courtesy
of Dr. J. J. Morgan

This result implies that humic substances also should be effective at promoting
rapid flocculation of hematite colloids, as is indeed observed experimentally.
Evidently a polymeric organic anion provokes rapid flocculation of positively
charged colloids when strongly adsorbed at low concentrations.

Figures 10.5 to 10.7 show collectively that, in the presence of surface
complex-forming ions, er p is the determining colloidal property for rapid floc-
culation. The existence of ions that can form surface complexes significantly
can be detected by examining ccc as a function of the initial colloid concentra-
tion. If charge screening is the principal cause of flocculation, the ccc will be
essentially independent of colloid concentration — at least over a severalfold
change — whereas if surface complexation is the principal cause, the ccc will
tend to increase with colloid concentration because the surface complexation
capacity is also increased. If the surface- complexing ion is multivalent, like
P0 4 ~ or Al 3+ , its strong adsorption can result in a reversal of the sign of a p .
When this happens, ions that previously were of the same charge sign as the
colloidal particles now become the flocculating ions. The mechanism of any
flocculation induced by these ions can be either charge screening or strong
adsorption.

When polymer ions (e.g., Al-hydroxy polymers or humus) form surface
complexes with soil colloids, stability depends on surface charge density. If the
extent of polymer adsorption is small, a soil colloidal suspension can become
flocculated at a lower concentration of indifferent electrolyte (like NaCI) than
in the absence of the polymer (Fig. 10.7)! In this situation, the addition of
electrolyte brings the now less-repelling colloidal particles closer together until
flocculation can occur at lower electrolyte concentrations than in the absence

Colloidal Phenomena 261

Table 10.1

Chemical factors that affect the stability of soil colloidal suspensions.

Chemical
factor

Affects

Promotes Promotes stability

flocculation when when

Electrolyte
concentration
pH value
Adsorption of
small ions
Adsorption of
polymer ions

Charge screening

Increased

Decreased

?H = p.z.c.

pH ^ p.z.c.

°p =

a p #0

Op =

a p #0

of the polymer. Alternatively, the colloidal suspension may be stabilized by the
repulsive electrostatic force between coatings of adsorbed polymers. Which
phenomenon occurs depends on the pH value, the electrolyte concentration,
and the configuration of adsorbed polymer ions.

The principal surface chemical factors that determine the stability of soil
colloidal suspensions are summarized in Table 10.1, with conditions that lead
to W = 1 listed in the third column. Particle surface chemistry universally
affects colloid stability through changes in the strength of the repulsive elec-
trostatic force. Rapid flocculation is the result of a reduction in this repulsive
electrostatic force, whether through charge screening or surface complexation.

10.5 Fractal Floccules

Electron micrographs of floccules comprising specimen oxide minerals have
been examined to determine the relationship between the number of primary
particles N they contain and their spatial extent as expressed by some length
scale, L. For example, L can be estimated by the geometric mean value of the
longest linear dimension of a floccule and the dimension that is perpendicular
to the axis of the former. Log— log plots of N versus L based on the examination
of many floccules show that a linear relationship typically obtains, implying
the power law:

N = AL

(10.22)

where A and D are positive parameters. This kind of power-law relation-
ship between floccule primary particle number and length scale has also been
observed in computer simulations of transport-controlled flocculation. In this
case, the simulated value of D is 1.78 ± 0.04.

The power— law relationship in Eq. 10.22 has implications for measure-
ments of floccule size and dimension during the flocculation process itself. If
the principal contributor to floccule growth is encountered between particles

262 The Chemistry of Soils

of comparable size, the increase in N per encounter will be equal approxi-
mately to N itself, and if colloid diffusion is the cause of these encounters, the
kinetics of flocculation will be described by a second-order rate law:

dN increase in N per encounter

timescale for encounter

NKseP = KsePo

(10.23)

where Kse is defined in Eq. 10.3 and po = Np is the initial number density, as
in Eq. 10.10. Equation 10.23 implies

N(t) = N(0) + KsEPot ~ K SE pot [t >> N(0)/K SE Po]

(10.24)

Taken together, Eqs. 10.22 and 10.24 yield a relationship between floccule
length scale and time:

L(t) ~ (K SE Po/A) 1/D

t 1 / D [t>>N(0)/K SE p ]

(10.25)

Figure 10.8 is a log-log plot of the average floccule diameter (as measured
by light-scattering techniques) versus time during the rapid flocculation of
hematite colloids by Cl _ or E^PO^ - (Figs. 10.4 and 10.6). The good linearity

A KCI= 100 mM

D =1.91 ±0.02

O P T = 32 fiM

1000 -

D = 1.87 ±0.03

J$Y&

Hematite

pH6

1 1 1 1 — 1 — 1 1 1

10
t (min)

100

Figure 10.8. Log-log plot of the average floccule diameter versus time for hematite
colloids suspended in either 100 mM KCL solution or 32[iM KH2PO4 solution at pH 6.
Floccule growth with time during rapid coagulation is the same in both suspensions,
leading to the same mass fractal dimension (D) for the floccules. Data from Chorover,
J. op. cit.

Colloidal Phenomena 263

1.2

■

1.0.
0.8.

V * ^

X V «o * Q
v o|.,H

. 06 ■

0.6.

i°

0.4.

Hematite
pH3

■ o PAA

0.2-

* v NaCI

40
t (min)

Figure 10.9. Plot of the average floccule diameter versus time for hematite colloids
suspended in either NaCI solution at the ccc or polyacrylate (PAA) solution at the p.z.c.
Floccule growth with time during rapid coagulation is essentially the same in both
suspensions. Data from Ferretti, R., J. Zhang, and J. Buffle (1997) Kinetics of hematite
aggregation by polyacrylic acid. Colloids and Surfaces 121A: 203-215.

of the plot confirms Eq. 10.25, whereas the excellent superposability of the
data shows the similar nature of the flocculation process at either the ccc or
the p.z.c. with respect to H2PO^j~. The two resulting values of the exponent D
agree within experimental precision. Comparable results have been reported
for silica and goethite colloids flocculating in 1:1 electrolyte solutions. Floc-
cule growth produced by rapid coalescence induced by the polymeric anion
polyacrylate (PAA, a polymer of acrylate,CH2 = CHCOO - ), is illustrated and
compared with that caused by Cl _ for hematite colloids atpH 3 in Figure 10.9.
The power— law shape of the time dependence of floccule diameter is appar-
ent, as is the expected independence from the type of coagulating anion of the
fractal dimension calculated with these data: D = 1.88 ± 0.02.

The power— law relation in Eq. 10.22 can be interpreted physically as the
characteristic of a mass fractal. The exponent D is then termed the mass fractal
dimension. Some basic concepts about mass fractals are introduced in Special
Topic 6 at the end of this chapter. Suffice it to say that Eq. 10.22 is a gener-
alization of the geometric relation between the number of primary particles
in a d-dimensional (d = 1,2, or 3) floccule and its d-dimensional size. For

264 The Chemistry of Soils

example, imagine a one-dimensional floccule portrayed as a straight chain of
circular primary particles, each of diameter Lo. The number of particles in a
chain of length L is then

N(L) = L/L = AL (10.26)

where A = 1/Lo in this case. Equation 10.26 has the appearance of Eq. 10.22,
but with D = 1. If the floccule is two-dimensional, it can be represented by a
parquet of circular primary particles packed together so that they touch. The
number of particles in the cluster will then be

N(L) = g(L/L ) 2 = AL 2 (10.27)

where now A = g/L 2 , and g is a geometric factor with a value that depends
on exactly how the circular primary particles have been packed. In this case,
Eq. 10.22 is recovered if D = 2. Evidently, Eq. 10.22 with 1 < D < 2 repre-
sents a floccule with fractal dimension D with a structure that is intermediate
between that of a chain and that of a parquet. If the floccule is a highly con-
voluted chain of particles, one that winds about in space but does not fill it,
then it is reasonable to suppose that the size-dimension relation in Eq. 10.22
could describe it with a noninteger value of D. Its ability to fill the plane
of view, irrespective of its shape, is quantified by how closely D approaches
the value 2.0.

Experimental measurements of the fractal dimension of floccules formed
by the rapid coalescence of specimen mineral colloids (oxides and clay min-
erals) typically fall in the range 1.2. to 1.9. These experimental values of D
are comparable with 1.7 to 1.8, the range of fractal dimension calculated for
floccules formed in a computer simulation in which colloids are permitted to
diffuse randomly with a Stokes-Einstein diffusion coefficient (Eq. 10.1) until
they collide, after which they coalesce instantly. The results also are compara-
ble with the range of D values inferred for atmospheric aerosols: 1.7 to 1.8.
Thus, the available data and calculations indicate that rapid coalescence leads
to floccules with a size that is a power-law function of time and with a fractal
dimension that lies in a narrow interval around 1.75.

Floccules formed under reaction control also are found to be mass fractals.
Figure 10.10 illustrates this fact for the hematite suspensions with a stability
ratio that is plotted against [KCl] in Figure 10.4. The values of D are seen to
decrease from about 2.1 to near 1.7 as W declines by an order of magnitude.
This decrease in the fractal dimension implies the concurrent development of
floccules with a space-filling nature that decreases. Denser floccules formed
more slowly permit time for colloids to seek out pathways of coalescence lead-
ing to more compact structures. A variety of studies has found that the fractal
dimension of floccules formed under reaction control lies in the range 1.9 to
2.1. These values are in agreement with computer simulations of coalescence
in which floccules with D ~ 2.0 to 2.1 are formed after assigning a very small
probability to coalescence after the collision of two particles.

Colloidal Phenomena 265

2.2

2.1

2.0
D 1.9
1.8
1.7
1.6

I I

Hematite
pH6

Figure 1 0. 1 0. Dependence of the mass fractal dimension (D) on the stability ratio (W)
for the hematite suspensions with flocculation kinetics behavior shown in Figure 10.4.
Data from Chorover, J. op. cit.

Measurements of the fractal dimension of floccules formed in the presence
of low concentrations of PAA, less than those required for rapid coalescence
(Fig. 10.9), lead to D ~ 1.9 to 2.1 as well, with the correspondingly denser
floccule structure then confirmed in electron micrographs. Thus, for PAA, a
transition of D from values near 2.1 to values near 1.8 occurs as the con-
centration of the polymeric anion increases, in parallel with the trend in
Figure 10.10.

As floccules go through drying and rewetting cycles to form aggregate
structures (Section 10.2), it is possible that they may retain their mass fractal
nature. An abundant body of literature now shows that this, indeed, is the case.
Perhaps the most direct experimental demonstration of the fractal nature
of soil aggregates is that based on the dependence of their bulk density on
aggregate size. Bulk density (pt>) is defined by the equation

mass of solids
volume

(10.28a)

where the numerator is the (dry) mass of the solid framework of an aggregate
and the denominator is its total volume, including pore space. If the aggregate
is a mass fractal, Eq. 10.22 applies and Eq. 10.28a becomes

BL L

)lur

(0 < D < 3)

(10.28b)

where B is a positive parameter that includes the density of the primary parti-
cles out of which the aggregate is built. Because the total volume of an aggregate
characterized by the length L is proportional to L 3 , Eq. 10.28b reduces

266 The Chemistry of Soils

0.2

■ Sharpsburg series
Mollisol
D = 2.945±0.013

log p b =0.1 62±0. 007-0. 055±0.01 3 log d .

0.1
0.01

±1_

±J_

0.1 1.0

d (mm)

Figure 10.11. Dependence of the dry bulk density of natural aggregates in the
Sharpsburg soil (fine, montmorillonitic, mesic Typic Argiudoll) on the average aggre-
gate diameter, showing behavior expected for a mass fractal with fractal dimension
D = 2.95. Data from Rieu, M., and G. Sposito (1991) Fractal fragmentation, soil
porosity, and soil water properties: II. Applications. Soil Sci. Soc. Am. J. 55:1239—1244.

to the power— law proportionality

Pb ocL

D-3

(10.28c)

Equation 10.28c shows that the bulk density of a mass fractal aggregate
decreases with increasing size, because D < 3. [If D = 3, then the aggregate is
not a fractal object, Eq. 10.28b becomes analogous to Eq. 10.27, and p\, is inde-
pendent of aggregate size.] Equation 10.28c is illustrated in Figure 10.1 1 for a
Mollisol with a clay fraction that is high in montmorillonite. Over the range
of aggregate diameters between 0.05 and 7 mm, the log-log plot of p\, versus d
(aggregate diameter) is linear with slope —0.055 ± 0.013 (i.e., D = 2.95). This
larger value of the fractal dimension, typical of clayey aggregates, indicates
their more space-filling structure.

For Further Reading

Baveye, P., J.- Y. Parlange, and B. A. Stewart (eds.). (1998) Fractals in soil
science. CRC Press, Boca Raton, FL. The first and sixth articles in
this compendium volume present comprehensive introductions to the
applications of fractal concepts to soil aggregates.

Buffle, J., K. J. Wilkinson, S. Stoll, M. Filella, and J. Zhang. (1998) A gener-
alized description of aquatic colloidal interactions. Environ. Sci. Technol.
32:2887-2899. A fine review of the structure and formation of floccules
by colloids in natural waters.

Hunter, R. J. (2001) Foundations of colloid science. Oxford University Press,
New York. A comprehensive standard textbook on colloid chemistry.

Colloidal Phenomena 267

Sposito, G. (1994). Chemical equilibria and kinetics in soils. Oxford Univer-
sity Press, New York. Chapter 6 of this advanced textbook provides a
discussion of the kinetics of fiocculation, including fractal aspects.

Sposito, G. (2004) The surface chemistry of natural particles. Oxford University
Press, New York. Chapter 5 of this advanced textbook contains a detailed
description of fiocculation and the light-scattering techniques used to
quantify both floccule formation and structure.

Wilkinson, K. J., and J. Lead (eds.). (2007) Environmental colloids and parti-
cles: Behaviour, separation, and characterisation. Wiley, New York. The 13
chapters of this comprehensive edited monograph provide broad surveys
of the current status of understanding colloidal structure and formation
in natural waters as well as emerging experimental methodologies for
exploring them.

Problems

The more difficult problems are indicated by an asterisk.

1. Calculate the diffusion coefficient of a soil colloid with radius l|xm that
moves through water at 25°C. According to an analysis by Albert Einstein,
the time required for a colloid to diffuse a distance Axis 2(Ax) 2 /3D. Esti-
mate the time required for the soil colloid to diffuse 10 |xm and compare
the result with the time required by an ion (see Special Topic 3 in Chapter 3
for a typical value of an ion diffusion coefficient).

2. A suspension consists of disk-shaped particles l|xm x l|xm x 10 nm,
each with a mass density of 2.5 x 10 kg m _ . Calculate the half-life for
perikinetic fiocculation at 25 °C in a quiescent suspension with an initial
solids concentration of 1 kg m -3 .

3. The data in the table presented here give the number density in a kaoli-
nite suspension during perikinetic fiocculation. Calculate the half-life for
fiocculation.

px1CT 14 (m- 3 ) Time(s) p x 1CT 14 (rrr 3 ) Time (s)

5.00
3.90
3.18
2.92

4. Equation 10.9 applies to a suspension that initially contains colloids with
the same radius R (i.e., a monodisperse suspension). If, instead, colloids of
radii Ri and R2 are present initially (i.e., a polydisperse suspension), the

2.52

335

105

2.00

420

180

1.92

510

255

1.75

600

268 The Chemistry of Soils

equation changes to have the form

where

dp - -,

R = (Ri + R 2 ) 2 /4R 2

and Di is the Stokes-Einstein diffusion coefficient of a colloid with radius
Ri. Calculate the rate coefficient at 25 °C for the flocculation of a mix-
ture of 1 ixm and 10 jxm colloids, then compare the result with the rate
coefficient for a monodisperse suspension of 1 |xm colloids. Note the
enhancement of the flocculation rate in the presence of the 10 |xm colloids.

"5. Suspensions of Ca-montmorillonite in chloride solutions show an anion
exclusion volume (see Section 8.4 and Problem 9 in Chapter 8) that
decreases to a limiting value near 3 x 10 m kg" as the chloride concen-
tration increases . Show that this limiting value implies complete exclusion
of chloride from a region between stacked layers with the opposing silox-
ane surfaces separated by 1 nm. (See Section 2.3 for an estimate of the
specific surface area of the clay mineral.)

6. Shown in the table presented here are values of W measured at pH 10.5
for a hematite suspension in the presence of varying concentrations of
either NaCl or CaCi2. Determine the ccc value in each electrolyte solution.
Why are they different? How well do they conform to the Schulze-Hardy
Rule (Eq. 10.17)?

[NaCI](mol

- 3 )

[CaCI :

1] (mol m 3 )

15.0

213

0.1

1.9

0.2

1.1

5.8

1.3

0.4
0.8

"7. A sample of slightly acidic soil (pH 6.4) with the exchangeable cation
composition ENa = 0.20 and Ek + Ec a + EMg = 0.75 was found to
disperse completely in water, whereas another sample of the soil taken
from elsewhere in the profile (pH 5.0, En s = 0.24, EK+Kc a +EMg = 0.61)
did not disperse. Use the concepts discussed in Section 10.4 to provide a
chemical explanation for these observations.

Colloidal Phenomena 269

"8. The turbidity of a colloidal suspension is its spatial decay parameter for
the transmission of a light beam through it:

It = I exp(-r£)

where I is the intensity of a beam incident on the suspension and I t is the
intensity of the beam after traveling a distance I through the suspension
while being scattered by floccules. Thus, x is mathematically analogous to
k in Eq. 10.12, in that the inverses of both parameters are characteristic
length scales over which a field phenomenon (electrostatic or electro-
magnetic) is attenuated. Models of the turbidity relate it to the number
of floccules in a suspension, allowing its rate of change with time to serve
as a quantitative measure of the rate of flocculation dp/dt, as in Eq. 10.9.
Usually this rate of change is determined as the slope of the initial por-
tion of a plot of t versus time as a suspension flocculates. Use the slope
data in the table presented here to estimate the ccc for a suspension of
hematite colloids in NaCl solution at pH 4.7. Identify the flocculating ion.
The value of At/ At corresponding to Kse (rapid flocculation, as in Eq.
10.9) is 0.016 s for unit length traversed by a light beam in the suspen-
sion. (Hint: Calculate W, then prepare a log— log plot of W against [NaCl]
analogous to that in Fig. 10.6.)

Ar/At(1CT 3 s- 1 ) [NaCl] (mol rrr 3 )

0.818 48

1.00 60

2.34 72

3.34 84

Shown in the following table are values of the stability ratio for the
hematite suspension in Problem 8, except that the NaCl concentration
is fixed at 5 mM, and 0.1 mg L _1 fulvic acid was added prior to turbidity
measurements. Determine the p.z.c. value for hematite under these con-
ditions. In the absence of fulvic acid, p.z.c. ~ 8.5. Does the p.z.c. value
you determined differ from 8.5? Why or why not?

W pH W pH

19.3

4.05

2.33

5.84

2.71

6.15

802

9.95

6.77

4.80

106

9.22

5.89

5.01

5.13

7.90

270 The Chemistry of Soils

*10. A suspension of birnessite (see Section 2.4) colloids at pH 1.40 showed
no observable particle migration as the result of an applied electric field.
A similar suspension of this Mn oxide mineral in the absence of an applied
electric field flocculated at pH 1.55. Explain why the two pH values can
be interpreted as giving essentially the same estimate of p.z.c.

11. Shown in the table presented here are values of the stability ratio for the
hematite suspension in Problem 9, except that the pH value is fixed at
6.9 and humic acid has been added. Determine a p.z.c. value for hematite
flocculation by humic acid.

W humic acid ((ig L 1 )

53.9 12.20

190 146.4

7.08 122.0

*12. Use concepts discussed in Sections 3.5 and 10.4 to explain the chemical
basis for the statement: "Organic matter prevents the dispersion of dry
soil aggregates; once the soil particles in the aggregates are forced apart
(by shaking in suspension), however, the organic matter helps to stabilize
the separated particles in suspension."

*13. The table presented here lists values of W at pH 4 for suspensions of
kaolinite particles containing adsorbed fulvic acid. Calculate the ccc for
each electrolyte solution. Why are the values of the ccc different? In your
response, consider the Schulze-Hardy Rule and the relevant p.z.n.c. values
for kaolinite and humus.

humic acid ((xg L

9.24

24.40

2.61

48.80

2.30

97.60

1181

244.0

[Ca(N0 3 ) 2 ]

[Cu(N0 3 ) 2 ]

[Pb(N0 3 ) 2 ]

(mol m~ 3 )

0.35

111

0.10

0.50

0.20

0.80

5.5

0.35

2.7

0.35

1.9

1.0

2.0

0.50

2.0

0.50

1.9

1.5

1.9

0.80

1.9

0.80

14. The table presented on the next page shows the average number of silica
particles in a floccule of radius R as measured during flocculation. Cal-
culate the fractal dimension of the floccules and determine whether the
flocculation process is transport controlled or surface reaction controlled.

Colloidal Phenomena 271

R (nm)

1.0

2.0

120

3.8

500

8.0

2200

10.5

4400

15. The data in the following table show the dependence of aggregate size
on bulk density for three soils of differing texture. Use linear regression
analysis to estimate the mass fractal dimensions of the aggregates in the
soils, including 95% confidence intervals on D.

Bulk density

Fine sandy loam

Silt loam

Clay

Mean size (mm)

(Mg rrr 3 )

(Mg m

4.200

1.49

1.42

1.49

1.595

1.58

1.68

1.025

1.75

1.68

1.70

0.715

1.82

1.61

1.73

0.505

1.94

1.72

1.75

0.335

2.17

1.75

1.80

0.200

2.11

1.82

1.75

0.125

2.15

2.10

1.80

Special Topic 6: Mass Fractals

The term fractal, coined by Benoit Mandelbrot 40 years ago from the Latin
adjective fractus (meaning broken), refers to the limiting properties of math-
ematical objects that exhibit the attributes of similar structure over a range
of length scales; intricate structure which is scale independent; and irregular
structure which cannot be captured entirely within the purview of classical
geometric concepts, use of a spatial dimension that is not an integer.

A flocculation process involves the coalescence of primary particles into
floccules. That this process can lead to a mass fractal can be illustrated by
constructing clusters from a primary particle comprising five disks, each of
diameter do (Fig. 10.12). The primary particle has a diameter equal to 3do-
If five of these units are combined to form a cluster with the same symmetry

272 The Chemistry of Soils

3 DIAMETERS

9 DIAMETERS

■ I 1 ' ""fr

4444

•H

♦■+

*4++

4-t-N-

27 DIAMETERS

81 DIAMETERS

Figure 10.12. A sequence of two-dimensional clusters constructed by combining five-
disk clusters (A) in such a way that their inherent symmetry is preserved at each level
of combination (B-D). In the limit of infinite cluster size, a mass fractal is formed with
fractal dimension D = In 5/ In 3 = 1.465.

as a single unit (i.e., each unit in the cluster is arranged like a disk in the
unit), the diameter grows to 9do (Fig. 10.12B). If five of these clusters are then
combined in a way that preserves the inherent symmetry (Fig. 10.12C), the
diameter increases to 27do. The clusters formed in this process exhibit similar
structure, complexity, and irregularity (Fig. 10.12D). Therefore they qualify as
fractal objects.

The size of each cluster in the sequence as expressed through the number
N of primary particles it contains is 5, 25, 125, and 625 for the four exam-
ples shown in Figure 10.12. Thus, N = 5", where n = 1,2, . . ., denotes the
stage of cluster growth. The diameter L = 3ndo, where n = 1,2, . . ., once
again. The relationship between these two properties — cluster size and cluster

Colloidal Phenomena 273

dimension — can be expressed mathematically as in Eq. 10.22:

N(L)=AL D (S6.1)

where A and D are positive parameters. In the current example, Eq. S6.1 has
the form

5 n = A(3 n d ) D (n= 1,2,...) (S6.2)

Thus, A = d^~ and

D = In 5/ In 3 Rs 1.465 (S6.3)

after substitution for A in Eq. S6.2 and solving the resulting expression for the
exponent D. More generally, if r denotes the scale factor by which the diameter
increases at each successive stage, then

D = lim - [In N (n) /In r] (S6.4)

nfoo n

defines the mass fractal dimension of a cluster with a size N(n) that is at any
stage. For the cluster in Figure 10.12, r = 3 and N(n) = 5 n , leading to the
fractal dimension given by Eq. S6.3.

The mass fractal dimension of a floccule is a numerical measure of its
space-filling nature. The clusters in Figure 10.11 occupy space in a plane (geo-
metric dimension = 2). If they were formed by disks arranged in a single row,
the mass fractal dimension that characterizes them should equal 1.0 because
they would be effectively one-dimensional objects. On the other hand, if they
were compact structures comprising closely packed disks, their mass fractal
dimension would equal 2.0, indicating a complete paving of the plane and
their space-filling nature. The mass fractal dimension of the clusters actually
is near 1 .5, meaning that the clusters have a porous structure that is not entirely
space filling.

This porous structure of a fractal can be quantified by estimating its
number density at any stage of growth. The bulk density (number per unit
area) of any cluster in Figure 10.12 can be calculated with the equation

p n = N(n)/(^L(n) 2 /4)

= (4A/7T)[L(n)] D - 2 (D < 2) (S6.5)

where Eq. S6.1 has been used, the area occupied by a cluster being 7rL 2 /4,
and L(n) = 3 n do is the diameter of the n cluster. Because D < 2, it follows
from Eq. S6.5 that p n decreases as n increases. In general, for a mass fractal in
E-dimensional space, the number density is given by a power-law expression
like Eq. 10.28c:

p(L) = bA L D_E (D < E) (S6.6)

274 The Chemistry of Soils

where b is an appropriate geometric factor (e.g., b = 4/it in Eq. S6.5).
Equation S6.6 shows that bulk density always decreases as size increases. This
can be used as an experimental criterion for evaluating whether a floccule or
an aggregate is a mass fractal object, as illustrated in Figure 10.11.

Soil Acidity

11.1 Proton Cycling

A soil is acidic if the pH value of the soil solution is less than 7.0. This condition
is found in many soils, perhaps half of the arable land worldwide, particularly
that under intensive leaching by freshwater, which always contains free protons
at concentrations above 1 mmolm -3 . Soils of the humid tropics offer examples
of acid soils, as do soils of forested regions in the temperate zones of the earth.
Soils in peat-producing wetlands and those influenced strongly by oxidation
reactions (e.g., rice-producing uplands) could be added as specific examples
in which the biota plays a direct role in acidification.

The phenomena that produce a given proton concentration in the soil
solution to render it acidic are complex and interrelated. (The quite separate
issue of measuring this proton concentration is discussed in Special Topic 7 at
the end of this chapter.) Those pertaining to sources and sinks for protons can
be considered schematically as a special case of Figure 1.2, with "free cation
or anion" in the center of the figure interpreted as H + . In addition to the bio-
geochemical determinants of soil acidity, the field-scale transport processes
wetfall (rain, snow, throughfall), dryfall (deposited solid particles), and inter-
flow (lateral movement of soil water beneath the land surface on hill slopes)
carry protons into a soil solution from external sources. Their existence and
that of proton-exporting processes (e.g., volatilization, erosion) underscore the
fact that the soil solution is an open natural water system subject to anthro-
pogenic and natural inputs and outputs that may by themselves dominate the
development of soil acidity. Industrial effluents (e.g., sulfur and nitrogen oxide

275

276 The Chemistry of Soils

gases or mining waste waters) that produce acidic deposition or infiltration
and nitrogenous fertilizers with transformation and transport that produce
acidic soil conditions are examples of anthropogenic inputs. Despite all this
complexity, proton cycling in acidic soils at field scales has been quantified
sufficiently well to allow some general conclusions to be drawn. Acidic depo-
sition, production of CC>2(g) and humus, and proton biocycling all serve to
increase soil solution acidity, whereas proton adsorption and mineral weath-
ering decrease it. Thus, over millennia, after readily "weatherable" minerals
become depleted, freshwater leaching (Fig. 2.6) can produce highly acidic
soils.

Carbonic acid (H2CO3) is a ubiquitous source of protons to soil solutions,
but one with a concentration that varies spatially and temporally because of
respiration processes. The formation of carbonic acid and its reactions in
the soil solution are discussed in Section 2.5, Problem 15 in Chapter 1, and
Problems 5 to 10 in Chapter 4. The key mathematical relationship with respect
to soil pH is presented in Problem 8 of Chapter 4:

Pco 2 / (H + ) (HCO~) = 10 7 - 8 (T = 298.15 K) (11.1)

Equation 11.1 shows that the partial pressure of CO2 (in atmospheres) and
the bicarbonate ion activity fully determine the pH value of the soil solution.
Numerical calculation is facilitated by writing the equation in logarithmic
form:

pH = - log (H+) = 7.8 + log (HCO") - log P C o 2 (11.2)

The pH value of an acidic solution comprising only H^COj", for which (H + )
closely approximates (HCO^~), can be calculated with Eq. 11.2 after Pco 2 * s
specified. For atmospheric air, Pco 2 ~ 10 -3,52 atm and pH = 5.7; for soil air
in B horizons or in the rhizosphere, Pco 2 ~ 10 -2 atm and pH = 4.9; and for
a flooded soil (Section 6.5), Pco 2 ~ 0.12 atm and pH = 4.4. Thus, pH values
varying within 0.7 log units of 5.0 can be expected in soil solutions if carbonic
acid dissociation is the dominant chemical reaction governing soil acidity.

A second major contributor to soil acidity is humus, whose proton
exchange reactions were introduced in Section 3.3 and were described quan-
titatively in Section 9.5 using the NICA— Donnan model. Humic substances,
a major fraction of humus, offer a large repository of acidic protons in the
form of carboxyl groups with pH^ values that are near 3.0 (Section 3.2).
For soils in which organic C is cycled intensively (e.g., Alfisols, Mollisols, and
Spodosols), the protonation-proton dissociation reactions of humus exert a
strong influence on acidity. The key capacity factors governing this influence
are total acidity (TA), cation exchange capacity (CEC), and acid-neutralizing
capacity (ANC), as defined in Section 3.3 and in Problem 7 of Chapter 3:

TA = CEC-ANC (11.3)

Soil Acidity 277

where

ANC = -er H (o-h < 0) (11.4)

when all quantities are expressed per unit mass of humus. Thus, TA (also
termed exchangeable acidity) is a quantitative measure of the capacity of soil
humus to donate protons under given conditions of temperature, pressure,
and soil solution composition. Cation exchange capacity being the maximum
moles of proton charge dissociable from unit mass of soil humus (i.e., the
carboxyl and phenolic OH protons that are displaceable according to a cation
exchange reaction like that in Eq. 3.4), TA can then be pictured as quantifying
the exchangeable protons that remain after a given negative value of net pro-
ton charge has been reached. This net proton charge is necessarily balanced by
adsorbed ion charge (Eq. 7.8) and, therefore, -an(cfH < 0) provides a quan-
titative measure of the capacity of soil humus to replace adsorbed ions with
protons under given conditions of temperature, pressure, and soil solution
composition.

If the NICA-Donnan model is applied to describe the relationship
between TA and CEC for, say, humus carboxyl groups, then Eq. 9.26 takes
the form

(K H c H ) PH
TA = CEC V " Hy xpH (11.5)

1 + (K H c H ) P

where Kh and pn are adjustable parameters discussed in Section 9.5, in which
specific values are given for humic substances. Equation 1 1.5 implies that TA
increases with the concentration of protons (ch) in the soil solution (i.e., it
increases with decreasing pH). According to Eqs. 11.3 to 11.5,

ANC = CEC - TA = CEC

\ (Khch)

1 + (k h c h )
CEC

1 + (Khch)

(11.6)

in agreement with the model expression for oh given in Problem 6 of Chapter 3 .
Thus ANC increases as ch decreases (i.e., it increases as pH increases), ulti-
mately approaching CEC. Note that Eq. 11.6 implies pH<j; s ~ logKn-

Buffer intensity ($h) is the derivative of ANC with respect to pH
(Section 3.3 and Problem 8 in Chapter 3). Operationally, Ph is the number of
moles of proton charge per unit mass that are dissociated from (complexed
by) soil humus when the pH value of the soil solution increases (decreases) by
1 log unit. The buffer intensities of organic-rich surface horizons in temperate-
zone acidic soils have maximal values in the range 0.1 to 1.5 mol c kg -1 pH -1
around pH 5, when expressed per unit mass of soil humus. Thus, for example,

278 The Chemistry of Soils

the addition of 20 mmol proton charge to a kilogram of soil with a humus con-
tent fh = 0.1 kgh kg , for which the buffer intensity is 0.2 mol c kgj~ pH ,
would decrease the pH by 0.02 mol c kg - ^(O.l kgh kg -1 x0.2 mol c kgj^ pH -1 )
= 1.0 unit. The relationship exemplified by this calculation is

ApH = An A /fh/3 H (11.7)

where An A is moles of proton charge added or removed per kilogram soil. Note
that, because Ph is pH dependent, ApH will be pH dependent. For example,
using the model expression in Eq. 11.6, one finds

dANC
3h =

CEC

dpH * dpH Ll + (K H 10-P H ) PH

(In 10) PH (K H 10-P H ) PH
= CEC- > '—

1+(K H 10-P H ) PH 1

= 2.303 p H ANC (11.8)

CEC

where the last step comes from In 10 = 2.303 and an appeal to Eqs. 11.5
and 11.6. Equation 11.5 implies that TA/CEC is a monotonically decreasing
function of pH that becomes negligibly small when pH > log Kh (see also
Problem 7 in Chapter 3), whereas Eq. 11.6 implies that ANC increases with
pH as the mirror image of total acidity. It follows from Eq. 11.8 that Ph
should then display a maximum at a pH value approximately equal to log Kh
appropriate for soil humus.

Adding complexity to this description of soil acidity and buffering are
the roles that Al- hydroxy polymers and the weathering of Al-bearing minerals
play (Section 11.3). Suffice it to say here that hydrolytic species of Al(III) — in
aqueous solution, adsorbed on soil particles (especially particulate humus), or
in solid phases — may strongly influence soil solution pH in mineral horizons
of acid soils. The buffer intensity they provide, however, is typically an order
of magnitude smaller than the values for soil humus.

The biological processes important in the development of soil acidity are
ion uptake or release and the catalysis of redox reactions. Plants often take up
more cations from soil than anions, with the result that protons are excreted to
maintain charge balance. For example, under the anoxic conditions that pre-
vail, peat bogs generate acidity because the vegetation takes up N either as NHj
or as fixed N2(g), thus inducing excess cation uptake and a resultant excretion
of protons to the soil solution. More generally, the rhizosphere may become
acidified relative to the soil in bulk because of proton excretion or organic
acid excretion, particularly those organic acids that have pH<jj s values less than
the ambient rhizosphere pH (Table 3.1). Under controlled experimentation,

Soil Acidity 279

rhizosphere pH values as much as 2 log units less than bulk soil values have
been measured. The influence on soil acidity from redox catalysis is discussed
in Section 1 1.4. It pertains essentially to the transformations of C, N, and S.

11.2 Acid-Neutralizing Capacity

Acid-neutralizing capacity as defined for soil humus in Eq. 11.4 refers to the
negative intrinsic surface charge produced by the exchange of complexed
protons for metal cations that, in principle, can themselves be displaced
subsequently by protons brought into the soil solution through any of the
acidity-producing processes discussed in Section 11.1. This latter possibility
is epitomized mathematically in the charge balance constraint that appears in
Eq. 7.8. For each mole of adsorbed metal cation charge removed from soil
humus, thereby causing Aq to decrease, a mole of complexed protons must
be added, causing oh to increase. This shift in adsorbed species captures pro-
tons from the soil solution while releasing adsorbed metal cations into the soil
solution.

Proton exchange reactions are not limited to soil humus, of course, and
accordingly it is possible to extend the concept of ANC to an entire soil adsor-
bent. This is done through the combination of operational definitions of TA
and CEC with a simple rearrangement of Eq. 11.3:

ANC = CEC-TA (11.9)

where total acidity is measured as the moles of titratable protons per unit
mass displaced from a soil adsorbent by an unbuffered KCl solution —
hence its alternative names: exchangeable acidity or KCl-replaceable acidity.
Experiments with a variety of mineral soils have shown that the principal
contribution to total acidity is made by readily exchangeable forms of Al(III):
Al 3+ , AlOH 2+ , Al(OH)+, and AlSO|. The protons released when these species
are displaced by K + and then hydrolyze in the soil solution are the titratable
protons measured experimentally. On the other hand, for soil humus, the
total acidity comprises mostly protons displaced from strongly acidic organic
functional groups or from adsorbed Al- and Fe-hydroxy species. The pH
dependence of TA for subsurface horizons of some acidic soils in the east-
ern United States is shown in Figure 11.1. The TA values were measured using
unbuffered KCl solution, whereas the CEC values were measured using BaCi2
solution buffered at pH 8.2. The ratio of TA to CEC declines sharply to zero as
pH increases above 5. This trend is typical of acidic mineral soils. By contrast,
TA for soil humus (Eq. 11.5) disappears well below pH 4.5. In Figure 11.1,
TA/CEC =_0.5 at pH ss 4.8, whereas Eq. 11.5 predicts TA/CEC = 0.5 at
pH ~ logKn ~ 2.3 to 2.9 for the strongly acidic functional groups in soil
humic substances (Section 9.5). Acid-neutralizing capacity exists in a soil solu-
tion for the same fundamental reason that it exists on a soil adsorbent (i.e., the

280 The Chemistry of Soils

0.6

0.4

TA
CEC

0.2 -

KCI - replaceable
acidity

•*■••■«.*-•

Figure 11.1. Total acidity (TA) as a fraction of cation exchange capacity (CEC) plotted
against pH for acidic mineral soils of the eastern United States.

presence of functional groups that can complex protons under acidic condi-
tions). For a soil solution in which carbonic acid is the only constituent that
provides these groups (in the forms of bicarbonate and carbonate anions),
ANC can be expressed by the equation

ANC = [HCO~] + 2 [CO^ _ ] + [OH - ] - [H+]

(11.10)

That Eq. 11.10 is analogous to Eq. 11.9 can be appreciated after noting the
logical correspondences (see Problem 7 in Chapter 4):

CEC & 2C0 3T = 2 [H 2 CO|] + 2 [HCO~] + 2 [CO3"] (11.11a)

TA & 2 [H 2 CO^] + [HCO~] + [H+] - [OH - ] (11.11b)

and applying them to Eq. 11.9. According to Problem 9 in Chapter 4, the first
two terms on the right side of Eq. 11.10 define the carbonate alkalinity. These
two terms are analogous to the two terms representing acidic functional groups
in soil humus that appear in the model equation for au presented in Problem
6 of Chapter 3. Thus, carbonate alkalinity refers to the carbonate anion charge
produced by the dissociation of complexed protons. The more general ANC
given by Eq. 11.10 is termed the alkalinity of a soil solution. However, if H2CO3
and water are the only compounds present, ANC given by Eq. 11.10 equals zero
because this equation is also the condition for charge balance in the solution.
The same situation arises if the ANC of an aqueous suspension containing only
particulate humus at concentration cs is considered:

ANC:

-o-HCs - cr d cs + [OH - ] - [H+] (cr H < 0)

(11.12)

where the first term on the right side is ANC contributed by the humus adsor-
bent (Eq. 3.7), the second term is titratable acidity contributed by protons

Soil Acidity 281

adsorbed in the diffuse-ion swarm, and the last two terms are ANC contributed
by the water in which the humus particles are suspended. Equation 11.12 is
the condition for charge balance in the suspension; hence its ANC is equal to
zero.

More generally, a soil solution will contain a variety of anions that proto-
nate and a variety of metal cations that hydrolyze in the acidic pH range. For
example, in the typical range 2 < pH < 6.5,

ANC = [HCO3-] + 2 [CO 2- ] + [HC2O7] + [H2PO4] + 2 [HPO4 ]

+ [OH - ] - [H+] - 3[A1 3+ ] - 2[AlOH 2+ ] - [Al(OH)+] (11.13)

which shows that protonating anions, including organic anions (Problem 1 in
Chapter 4), increase ANC, whereas hydrolyzing metal cations decrease ANC
of a soil solution. Charge balance in this example would be expressed typically
by the equation

[Na+] + [K+] + 2 [Ca 2 +] + 2 [Mg 2 +] + 2 [Fe 2 +] + 2 [Mn 2 +]
+ 3 [Al 3+ ] + 2 [AlOH 2+ ] + [Al (OH)+] + [H + ] - [OH - ]
" [ Cl ~] " [ N °3~] " 2 [ s °4~] " [HCO3-] - 2 [CO 2 "] - [HC 2 07]
- 2 [C 2 2 "] - [H 2 PO"] - 2 [HPO 2 -] = (11.14)

The combination of Eqs. 11.13 and 11.14 leads to an alternative equation for
ANC of a soil solution:

ANC = [Na+] + [K+] + 2[Ca 2+ ] + 2[Mg 2+ ] + 2 [Fe 2+ ] + 2[Mn 2+ ]

" [ Cl ~] " [ N °3~] " 2 [ S0 4 _ ] " 2[C 2 2 "] (11.15)

(Equations 11.13 to 11.15 neglect any nonhydrolytic metal complexes formed
by the cations and anions considered; however, adding them is straightfor-
ward.) Equation 11.15 is illuminating in that it implies that removal of metal
cation charge from a soil solution decreases its ANC, whereas removal of anion
charge increases its ANC, provided that the metal cations do not hydrolyze
and the anions do not protonate over the acidic pH range considered. These
effects are analogous to those occurring on a humus adsorbent as epitomized
in Eq. 7.8: Removing metal cation charge is equivalent to supplying proton
charge, but removing anion charge is equivalent to removing proton charge
from a soil solution. Conversely, adding anion charge through acidic deposi-
tion (NOj - and S0 4 _ ) or biological production (C20 4 _ , oxalate) is equivalent
to adding proton charge.

282 The Chemistry of Soils

11.3 Aluminum Geochemistry

Low soil pH is accompanied by proton attack on Al-bearing minerals (Fig. 5.1)
leading to the production of soluble Al(III) in the soil solution (Table 4.4). The
free-ion species of this soluble Al will equilibrate with soluble complexes (e.g.,
Al-oxalate complexes, as in Eq. 1.4 and Table 4.4 — see also problems 6 and

14 in Chapter 1); with the soil adsorbent; and, of course, with soil minerals.
Aluminum solubility in acidic soils is influenced by a variety of minerals that
are discussed individually in sections 2.3, 2.4, 5.2, and 5.4: gibbsite, kaolinite,
allophane/imogolite, pedogenic chlorite or beidellite, and hydroxy- interlayer
vermiculite or vermiculite. Dissolution reactions for these minerals are dis-
cussed in sections 2.3, 5.1, 5.2, and 5.4, as well as in problems 12, 14, and

15 of Chapter 2; and Problems 9, 10, 13, and 14 of Chapter 5. They are the
essential input used to construct activity-ratio diagrams similar to that in
Figure 5.5. The mineral with an activity-ratio line that lies highest in the dia-
gram is assigned control of Al 3+ activity, although metastability can intervene
to require interpretation using the GLO Step Rule (Section 5.2).

Metastability, in fact, appears to be the rule with respect to Al solubility
control in soils affected by acidic deposition or infiltration. The role it plays
can be illustrated by consideration of the dissolution reactions of gibbsite,
proto-imogolite allophane, and kaolinite:

Al(OH) 3 (s) + 3H+ = Al 3+ + 3H 2 (I) (11.16a)

-Si 2 Al 4 Oio • 5H 2 (s) + 3H+ = Al 3+ + -Si(OH)^

+ -H 2 0(£) (11.16b)

-Si 2 Al 2 5 (OH) 4 (s) + 3H+ = Al 3+ + Si(OH)° + -H 2 (£) (11.16c)

The dissolution equilibrium constants for these reactions each can vary over
one or two log units, with the larger values associated with poorer crystallinity
and, therefore, greater solubility of Al at a given pH value. Taking gibbsite
and kaolinite as examples, one can derive activity-ratio equations for log
[(solid)/(Al + )] as described in Section 5.2:

log [(gibbsite) / (Al 3+ )] = - log *K so + 3pH + 3 log (H 2 0) (11.17a)
log [(kaolinite) / (Al 3+ )] = - logK so + 3pH + log (Si(OH)°)

+ ^log(H 2 0) (11.17b)

where the first term on the right side is determined by the degree of crys-
tallinity of the mineral dissolving. For gibbsite, log* K so = 8.77 if the mineral

Soil Acidity 283

is reasonably well crystallized, 9.35 if it is in microcrystalline form, and 10.8 if
it is amorphous. For kaolinite, log K so = 3.72 if the mineral is well crystallized
and 5 .25 if it is not. This variability leads to the "windows" of mineral stability
discussed in Section 5.2.

At pH 5 and above, Al tends to precipitate in acidic soils and, because unit
water activities are expected, Eq. 11.17 specializes to the working equations

log [(gibbsite) / (Al 3+ )] = 15.0 - log *K so (11.17c)

log [(kaolinite) / (Al 3+ )] = 15.0 - log K so + log (Si(OH)°) (11.17d)

After the values of the dissolution equilibrium constants are selected,
Eqs. 11.17c and 11.17d can be plotted as in Figure 5.5. Figure 11.2 shows such
an activity— ratio diagram with the gibbsite and kaolinite windows included.
Allophane and the 2:1 clay minerals, also candidates for influencing Al solu-
bility, would typically plot within the kaolinite window, but with less strong
dependence on (Si(OH)°) than the smectite whose dissolution reaction
appears inEq. 5.18a because of lower Si- to-Al molar ratios, another character-
istic of acidic soil environments. Allophane would show a weaker dependence
on (Si(OHm than even kaolinite, but still would fall within the kaolinite
window. A solubility window for solid-phase silica like that in Figure 5.5 also
has been included in Figure 11.2, with amorphous silica depicted at its left
boundary and quartz at its right boundary.

At pH 5, Al solubility control falls to well- crystallized kaolinite over the
range of (Si(OH)°) shown (upper diagonal line). This result may be con-
trasted with that in Figure 5.5, which shows gibbsite taking over Al solubility

pH 5

(H 2 0) = 1

- log (Si(OH)O)

Figure 1 1.2. An activity-ratio diagram for Al solubility control at pH 5 by kaolinite
or gibbsite, with solubility "windows" shown for each mineral and for silica solubility
control by amorphous silica (left vertical line) to quartz (right vertical line).

284 The Chemistry of Soils

control at (Si (OH) 4 ) > 10 . This difference arises solely because of the
higher value of log *K so for well-crystallized gibbsite (8.77 vs. 8.11) used in
Figure 11.2, and it is significant: Silica leaching to a concentration less than
10 yumol L _1 is now required to stabilize well- crystallized gibbsite. On the other
hand, if kaolinite is poorly crystallized, well- crystallized gibbsite takes over sol-
ubility control at (Si (OH) 4 ) > 10 and even microcrystalline gibbsite can
do this at (Si (OH) 4 ) below that sustained by quartz. Spodosols tend to sup-
port silica solubilities near that of quartz and, therefore, are expected to show
Al solubility control by gibbsite, implying concentrations in the miilimore per
cubic meter range. Oxisols and Ultisols tend to show silica solubilities between
those of quartz and amorphous silica, thus opening the door to Al solubility
control by kaolinite, particularly if gibbsite precipitation is impeded by the
presence of strongly complexing organic functional groups that render Al 3+
unavailable for hydrolysis.

The near confluence of the lines in Figure 11.2 for quartz, poorly
crystallized kaolinite, and microcrystalline gibbsite is noteworthy for the-
oretical reasons. If log*K so for microcrystalline gibbsite were just 0.1 log
unit smaller (i.e., slightly better crystallinity), the horizontal line depicting log
[(gibbsite)/(Al 3+ )] for it would have intersected the vertical quartz solubility
line at (Al ) = 10 -5 ' 75 , which is where the diagonal kaolinite line intersects it
[introduce logK so = 5.25 and log (Si (OH)') = -4 into Eq. 11.17d]. Under
this condition, eqs. 11.16a and 1 1 . 16b can be combined with the corresponding
expression for quartz to yield the chemical equation

Si0 2 (s) + Al(OH) 3 (s) = -Si 2 Ai205(OH) 4 (s)+-H 2 0(£) (11.18)

This reaction can be interpreted as the formation of an inorganic condensation
polymer (Section 3.1), kaolinite, from its component oxide minerals. It is
straightforward to show that log K = for the reaction if log *K so = 9.25 for
gibbsite dissolution. This value, in turn, would require (H2O) = 1, as has been
already assumed in Figure 11.2.

If one now imagines that the only aqueous solution species in the soil
solution are those appearing in Eq. 11.16 [Al 3+ , H + , and Si(OH) 4 ], then
the four species appearing in Eq. 11.18 suffice as components for the system
under consideration. That is, eqs. 1 1 . 1 6a and 1 1 . 1 6c, along with the dissolution
reaction for quartz, are sufficient to describe the formation of all seven species
from the four components. Thus, equilibrium is completely determined by
the three relevant equilibrium constants and the fixed activities of the three
minerals plus liquid water. If the activity of the liquid component were not
1.0, equilibrium as portrayed in Eq. 11.18 would not be possible. Indeed,
log K = for the reaction means that poorly crystallized kaolinite and water
are not distinguishable thermodynamically from quartz and microcrystalline
gibbsite, in the same sense that hydronium ion (H30 + ) is not distinguishable
thermodynamically from a water molecule and a proton (Table 6.2).

Soil Acidity 285

Besides the monomeric Al species indicated in Table 4.4, evidence exists
for relatively stable polynuclear Al species, particularly in complexes with
OH - and organic anions. These polynuclear Al-hydroxy species, ranging
from AI2 (OH 2 ) to [Al04Ali.2(OH)24] 7+ , can engage in acid-base reactions
as aqueous solutes or in adsorption reactions on both soil humus and soil
minerals. The formation of hydroxy- interlayer vermiculite and pedogenic
chlorite involves the adsorption of Al-hydroxy polymers as the first step
(Section 2.3). These polymer coatings may affect Al solubility very similarly to
the relationship between (Al + ) and pH that obtains for gibbsite (Eq. 11.17a).

Given the kind of aqueous-phase speciation data listed in Table 4.4, the
distribution of exchangeable cations can be calculated if a Vanselow selectivity
coefficient has been measured (Section 9.3). Consider, for example, the analog
of Eq. 9.14 for Ca— Al exchange:

3 CaX 2 (s) + 2 Al 3+ = 2 AlX 3 (s) + 3 Ca 2+ (11-19)

The Vanselow selectivity coefficient (Eq. 9.18) is

4 a/A1 = xi 1 (Ca 2 +) 3 /xL(Al 3+ ) 2 (11.20)

Ca/Al

where the mole fraction xc a refers to CaX2, and xai refers to AIX3 . If K v has
been measured and found not to depend significantly on xc a > then Eq. 1 1.20
can be used to calculate the mole fraction of exchangeable Al 3+ that is in
equilibrium with the soil solution. Suppose, for example, that, in the Spodosol

Ca/Al

to which Table 4.4 applies, K y ~ 1.0 and is independent of xc a (i-e-> the
Vanselow model applies). Then, with (Al 3+ ) = 1.1 x 10" 6 and (Ca 2+ ) =
2.64 x 10~ 4 , based on Table 4.4 (and Eq. 4.24 with I = 2.03 mol m~ 3 ), one
calculates from Eq. 11.20

1.0= LlSfx^/Cl-XM) 3 ]

which implies that xai ~ 0.41. Thus, under the conditions given, neither
exchangeable cation is predicted to dominate the soil adsorbent, although

~ . Ca/Al

the value of E^y is only 0.005. [Note that K v = 1.0 corresponds to no
thermodynamic preference in the cation exchange reaction (Section 9.3)!]

The competition between protons and Al + for carboxyl groups on soil
humus can be described using the NICA-Donnan model as discussed in
Section 9.5. For humic acid, model parameters for the proton (logK; =
logKH = 2.93, pj = PhP = 0.5) are in a table preceding Eq. 9.29. Those
for Al 3+ are log Kai = 2.00 and p A1 = 0.25. Given fJ H = 0.81, derived from
extensive data analysis yielding the model parameters tabulated in Problem
15 of Chapter 9, it follows that p = 0.62 in Eq. 9.29. According to Table 4.4,
ch ~ 48 mmol m and cai ~ 1.8 mmol m . With these data as input, the
second factor on the right side of Eq. 9.29 is found to be 0.607, whereas the
third factor equals 0.423. Their product is the charge fraction of complexed

286 The Chemistry of Soils

Al + (qAj/bAi), about 0.26 under the conditions given (i.e., pH 4.3 and micro-
molar Al + ). Thus about one fourth of the carboxyl groups are predicted to
complex Al 3+ at pH 4.3. [Note that Pai/Ph = 0.31, as expected from the dif-
ference in valence of the two competing cations, such that b^i ~ 0.3bH, where
bn = bi = 3.15 mol c kg - according to the table preceding Eq. 9.29.]

Mineral dissolution reactions like those in Eq. 11.16 consume protons
and bring metal cations and neutral silica into the soil solution, thereby con-
tributing to its ANC while depleting that of the soil solids. This depletion is
reflected in a common field observation that the decrease in ANC of soil solids
is approximately equal to the net proton flux consumed by mineral weather-
ing. The same effect accompanies the cation exchange reaction in Eq. 11.19
(understood to proceed from left to right), because Al 3+ removal from the
soil solution increases its ANC and decreases the ANC of the soil adsorbent
(Eq. 1 1.9; loss of Al 3+ through adsorption implies an increase in total acidity.)
In this "trade-off" sense, the complexation of Al 3+ by soil humus, although it
reduces the toxic effect of this metal cation, does not alter the total acidity of
the humus, or the ANC of the soil solution, if it proceeds by a proton exchange
reaction, as in the example based on Eq. 9.29.

11.4 Redox Effects

In Section 6.2, it is emphasized that most of the reduction half-reactions that
occur in soils result in proton consumption (Eq. 6.7). Therefore, an important
source of ANC in soil solutions are the redox reactions that feature a net proton
consumption and effective microbial catalysis. More specifically, if a selected
reduction half-reaction couples strongly to the oxidation of soil humus, as
exemplified by the reverse of the penultimate reaction in Table 6.1, and if
the stoichiometric coefficient of H + in the selected reduction half-reaction is
larger than 1.0, the resulting redox reaction will deplete the soil solution of
protons. For example, denitrification, depicted by the redox reaction

4N07 + 5CH 2 + 4H+ = 2 N 2 (g) + 5 C0 2 (g) + 7 H 2 (1) (11.21)

consumes 1 mol H + mol -1 N produced as N 2 (g). Similarly, the reductive
dissolution of Fe(OH)3(s) in a flooded soil consumes 2 mol H + mol - Fe +
produced. Both of these redox reactions increase the ANC of the soil solution
(Eq. 11.15). [The production of C0 2 (g) in Eq. 11.21 does not affect ANC
because of the condition imposed by charge balance on a solution of H 2 CC>3
(Eq. 11.10).] Note that denitrification causes the removal of a nonprotonat-
ing anion without the simultaneous loss of a nonhydrolyzing metal cation,
whereas reductive dissolution causes the addition of a nonhydrolyzing metal
cation without the simultaneous production of a nonprotonating anion (see
Eq. 11.15).

Field studies have indicated the importance of the reactions in Table 6.1 to
the generation of ANC in the soil environment. Indeed, reductive dissolution

Soil Acidity 287

reactions involving Fe and Mn are examples of an increase in ANC caused by
mineral weathering. Because the seven principal redox-active elements in soils
(Section 6.3) also are essential elements for the nutrition of green plants, how-
ever, the ultimate impact of their redox reactions cannot be estimated without
full consideration of their biogeochemical cycles. For example, the uptake of
nitrate or sulfate by plant roots is balanced by the exudation of hydroxide ion
or bicarbonate into the soil solution, thus increasing ANC (Eq. 11.13). The
uptake of cations like Na + or Fe 2+ by plant roots is balanced by their exuda-
tion of H + , which decreases ANC. This latter process usually dominates with
respect to the net moles of ion charge entering roots, with a resultant acidifi-
cation of the soil solution and, ultimately, of the rhizosphere (Section 11.1).
Assimilatory nitrate reduction by bacteria increases ANC, as does dissimila-
tory nitrate reduction (Section 6.2). A more subtle example is provided by
the transformation of urea, (NH2)2CO, the nitrogenous fertilizer most widely
applied in agriculture worldwide, especially in wetlands rice cultivation. Urea
is converted rapidly to NHJ" and C0 2 (g) by hydrolysis and protonation:

(NH 2 ) 2 CO + 2 H+ + H 2 (I) = 2 NH+ + C0 2 (g) (11.22)

This conversion consumes 1 mol H + per mole of N produced as NH^~.
Subsequent uptake of ammonium by plant roots provokes the exudation of
charge-balancing protons that replace those consumed in urea hydrolysis. If
instead the NHJ" produced by urea hydrolysis is oxidized to form NO^~, 2 mol
H + are released into the soil solution per mole of N produced as nitrate ions:

NH+ + 2 C0 2 (g) + H 2 (£) = NO" + 2 CH 2 + 2 H+ (11.23)

This means that the overall transformation of urea to nitrate would yield a net
1 mol H + to the soil solution. However, the subsequent uptake of the nitrate
by plant roots results in the exudation of OH - or HCO^~ that neutralizes the
effect of H + released by the oxidation of NH^~. Thus the ANC of the soil solu-
tion has not been changed by the reactions ineqs. 11.22 and 11.23, if the nitrate
ions produced are entirely consumed by plants. Even if loss by denitrification
(Eq. 1 1.21) is the fate of the nitrate produced, this result holds true, because
denitrification consumes directly the excess 1 mol H + released by the combi-
nation of reactions in eqs. 11.22 and 11.23. Nitrate loss from the soil solution
by leaching, however, can reduce ANC if charge-balancing metal cations are
leached as well, thus leaving a net 1 mol H + added to the soil solution.

Besides producing C0 2 (g), which has no net effect on ANC, mineral-
ization of soil humus can reduce the ANC of a soil solution through the
production of NO^~ and S0 4 ~ (Eq. 11.15). This effect can be diminished by
removal of aboveground biomass before mineralization (e.g., harvesting of
agricultural crops). Reduced-N fertilizers, like NH4NO3 and (NH4) 2 SC>4, can
decrease soil solution ANC via oxidation, as in Eq. 1 1 .23 . Long-term field stud-
ies on fertilized plots have shown that NH4NO3 and (NH4) 2 S04 applications
in particular can decrease ANC greatly through nitrification. Ammonium

288 The Chemistry of Soils

sulfate and reduced-S species, often introduced into soils by dry deposition,
can produce decreases in ANC by subsequent oxidation. These processes may
account for half the input of protons into soil from atmospheric deposition
sources. The examples here thus serve to illustrate the broad scope of redox
effects on soil acidity, as well as the strong interrelatedness of the proton cycling
components identified in Section 11.1.

11.5 Neutralizing Soil Acidity

The processes that increase the pH value of a soil solution are mineral weath-
ering, anion uptake by the biota, protonation of anions or surface functional
groups, adsorption of nonhydrolyzing metal cations, and reduction half-
reactions. In acidic soils, these processes may not be adequate to maintain
pH in an optimal range if acidic deposition intrudes or acidifying fertilizers
are applied. When soil pH is such that the corresponding total acidity exceeds
about 15% of the CEC (Fig. 11.1), a variety of serious problems for plant and
microbial growth (e.g., Al, Fe, and Mn toxicity or Ca, Mg, and Mo deficiency)
is expected. Under this deleterious condition, soil amendments to decrease
total acidity must be considered.

The practice of neutralizing soil acidity is formalized in the concept of the
lime requirement. This key parameter is defined formally as the moles of Ca 2+
charge per kilogram soil required to decrease the total acidity to a value deemed
acceptable for an intended use of the soil. Because of the relatively unique
relationship between total acidity and pH typified by Figure 11.1, decreasing
total acidity to zero and, therefore, increasing pH to 5.5 and above, offers
a general, straightforward criterion for application of the lime requirement
concept to a broad range of mineral soils. Typically the lime requirement is
expressed in the convenient units of centimoles of charge per kilogram and is
found to have a value somewhere between that of the total acidity and the CEC
of a soil as measured with a buffered solution of BaCi2 (Section 11.2). It is
clear that the lime requirement will depend on soil parent material mineralogy,
content of clay and humus, and the Jackson— Sherman weathering stage of a
soil (Section 1.5). Special consideration also must be given to soils enduring
chronic proton inputs from acidic deposition and acidifying fertilizers.

Methods for measuring the lime requirement are described in Methods of
Soil Analysis (see "For Further Reading" at the end of this chapter). The proce-
dures that have been used range from field applications of CaC03 (involving
years to achieve a steady state), to laboratory incubations of soil samples with
CaC03 (involving weeks to months), to soil titrations with Ca(OH)2 over sev-
eral days, to rapid soil equilibrations (< 1 hour) with buffer solutions with
a composition that has been optimized for use with a given group of soils.
Considerations such as the number of soil samples to be analyzed with the
accuracy of the estimated lime requirement enter into the choice of method.

Soil Acidity 289

The fundamental chemical reaction underlying the concept of the lime
requirement appears in Eq. 11.19. This reaction, reversed so that CaX2(s)
and Al 3+ are the products, can be coupled with the dissolution reactions
of a Ca-bearing mineral added as an amendment, and an appropriate Al-
bearing mineral that precipitates, to produce an overall reaction that removes
Al + from the soil solution (see Problem 12 in Chapter 2 for a case involving
beidellite as an adsorbent). For example, if CaC0 3 (s) is added and Al(OH)3(s)
precipitates in response, one can combine eqs. 5.3, 11.16a, and 11.19 to obtain
the overall reaction

2 A1X 3 (s) + 3 CaC0 3 (s) + 3 H 2 (£)

= 3 CaX 2 (s) + 2 Al(OH) 3 (s) + 3 C0 2 (g)

(11.24)

Note that the equilibrium constant for this reaction provides a relationship
between adsorbate composition and the partial pressure of carbon dioxide,
if the two mineral phases and liquid water have unit activity. Evidently the
reaction will not affect the ANC of the soil solution, if it goes to completion,
but the ANC of the soil adsorbent will be increased. If the Al + that exchanges
for Ca + does not precipitate, on the other hand, the ANC of the soil solution
will decrease, as can be deduced from Eq. 11.13.

If the reaction in Eq. 11.24 occurs in a soil, the activities of Al 3+ and
Ca + in the soil solution are governed by Eq. 5.10 and an expression for the
thermodynamic cation exchange constant (Section 9.3):

K^ /A1 = (A1X 3 ) 2 (Ca 2+ ) 3 / (CaX 2 ) 3 (Al 3+ ) 2 (11.25)

These two equations can be combined to derive the relationship

pH + \ log (Ca 2 +) = \ log

*v 2i^Ca/Al

+ - log[(CaX 2 ) 3 / 2 /(AlX 3 )]

(11.26)

The left side of Eq. 1 1.26 is called the lime potential, an activity variable equal
to one half the common logarithm of the IAP of Ca(OH) 2 (s) (Section 5.1).
As a rule of thumb, soils that have adequate ANC have lime potentials greater
than 3.0. Equation 11.26 shows that the lime potential depends sensitively on
the activities of CaX 2 (s) and AlX3(s) on the soil adsorbent. The application
of Eq. 1 1.26 to soil acidity perforce requires a relationship between these two
activities and the charge fractions of CaX 2 (s) and AlX 3 (s) (Section 9.2). For
example, the linear regression equation

log (Ca 2 +) 3 /(Al 3+ ) 2

-0.74+ 1.02 ±0.07

X l0£

E CaX 2 /E ~

A1X,

(R 2

(11.27)

290 The Chemistry of Soils

describes the relationship between soil solution activities and charge frac-
tions of adsorbed Ca and Al in the A horizons of Spodosols. This empirical

Ca/Al

equation is tantamount to setting K ex ~ 0.2 in Eq. 11.25 while replacing
activities on the soil adsorbent by charge fractions. If *K so ~ 10 is assumed
(Section 11.3), then Eq. 11.26 reduces to the predictive equation

pH + l - log (Ca 2+ ) = 3.0 + l - log [E^/E^

(11.28)

It follows from Eq. 11.28 that the lime potential will be more than 3.0 if the
charge fraction of adsorbed Ca + is > 0.57.

For Further Reading

Alpers, C. N., J. L. Jambor, and D. K. Norstrom (eds.). (2000) Sulfate min-
erals. Mineralogical Society of America, Washington, DC. Chapter 7 of
this edited workshop volume gives a comprehensive review of Fe and Al
mineral formation in acidic waters dominated by sulfate inputs.

Ehrenfeld, J. G., B. Ravit, and K. Elgersma. (2005) Feedback in the plant-soil
system. Annu. Rev. Environ. Resour. 30:75-115. This thought-provoking
review describes, among other things, the influence of plants on soil
acidity and redox conditions.

Essington, M. E. (2004). Soil and water chemistry. CRC Press, Boca Raton,
FL. Chapter 10 of this textbook provides a thorough introduction to soil
acidity, including that induced by sulfur oxidation in pyritic materials.

Rengel, Z. (ed.). (2003) Handbook of soil acidity. Marcel Dekker, New York.
This edited monograph provides useful surveys of the causes, effects, and
management of soil acidity at an advanced level.

Sparks, D. L. (ed.). (1996) Methods of soil analysis: Part 3. Chemical methods.
Soil Science Society of America, Madison, WI. Chapter 1 7 of this standard
reference describes methods to measure the lime requirement of soils.

Sposito, G. (ed.). (1996) The environmental chemistry of aluminum. CRC Press,
Boca Raton, FL. The 10 chapters of this edited volume provide a detailed
account of Al geochemistry in acidic soils and waters, including the effects
of acidic deposition.

The following articles give valuable research-oriented discussions of chemical
processes in acidic soils and waters.

Chadwick, O. A., and J. Chorover. (2001) The chemistry of pedogenic

thresholds, Geoderma 100:321-353.
Driscoll, C. T, et al. (200 1 ) Acidic deposition in the northeastern United States:

Sources, inputs, ecosystem effects, and management strategies. Bioscience

51:180-198.

Soil Acidity 291

Problems

The more difficult problems are indicated by an asterisk.

1. Use the concept of charge balance and the data in Problem 7 of Chapter
4 to verify that (H + ) = (HCO^) in a pure solution of H2CO3. [Hint:
Calculate (H + ) for the range of Pco 2 typical of soils using Eq. 11.2 and
the assumption that (H + ) = (HCO^~). Then show that, for the range of
(H+) calculated, [OH - ] and [CO3"] are negligible.]

2. State whether the addition of a small amount of each of the following
compounds to a soil solution will increase, decrease, or not change its
ANC. Explain your conclusion in each case.

a. C0 2 c. Si(OH) 4 e. Na 3 P0 4

b. NaN0 3 d. H 2 S0 4 f. CH3COOH

3. The buffer intensity of soil collected from an A horizon (fj, = 0.10) is 1.5
mol c kgh~ pH at pH 4.0. Calculate the moles of proton charge per
kilogram soil that must be removed to raise the pH value by 0.5 log units.

*4. In the table presented here are data on the buffer intensity at pH 4.5 for
surface and subsurface horizons of Spodosols with varying humus con-
tent. Calculate Ph from the relationship between soil buffer intensity and
humus content. What change in pH is expected for an input of 92 mmol
of proton charge per kilogram of soil?

Buffer intensity

Buffe

r intensity

f h (kg h kg 1 )

(mol c kg~ 1 pl-r 1 )

f h (kg h kg 1 )

(mol c

kg- 1 pl-r 1 )

0.103

0.0088

0.054

0.0054

0.162

0.0166

0.102

0.0084

0.030

0.0068

0.038

0.0054

0.902

0.0738

0.401

0.0416

0.947

0.0824

0.870

0.1122

5. The ratio of ANC to CEC for O horizons of Swiss Inceptisols was observed
to depend linearly on pH:

ANC , , .

= 0.57 pH - 1.38 (R 2 = 0.90)

CEC v v '

a. Calculate the soil buffer intensity range that corresponds to CEC in
the range for Inceptisols (Table 9.1).

b. Plot TA/CEC against pH in the range 3.0 to 4.0. At what pH value is
TA/CEC = 0.5?

292 The Chemistry of Soils

6. Given that NH)J~ uptake by plants usually produces excess cation over
anion uptake, and that NO^~ uptake usually produces the opposite effect,
what is the expected change in rhizosphere pH from the uptake of each
N species?

7. Long-term field experiments indicate that acidic soils receiving nitrogen
fertilizer as (NH^SG^ decrease in pH, whereas those receiving NaNC>3
increase in pH. Give an explanation for these results in terms of the ANC
of the soil solution and all the processes described in Section 11.1. (You
may neglect deposition processes.)

*8. The following table shows the changes in exchangeable metal cation
charge (mmol c kg -1 ) in the O horizons of several forest soils as their
pH values were decreased gradually to pH 3.0 by addition of dilute HCl
solution.

a. Calculate the loss of soil adsorbent ANC resulting from the acid input.

b. Estimate the buffer intensity of each soil at pH 3.

(Hint: Assume that CEC as well as ANC changes after the pH value is
decreased to 3.0)

Initial pH Al 3 + Ca 2 + Fe 2 + H+ K+ Mg 2 + Mn 2 +

3.49

0.0

-5.8

-0.8

+5.6

+2.6

-1.6

+0.1

3.60

-5.5

+4.2

-0.6

-4.6

+ 1.3

-1.6

-0.2

3.64

-2.1

-29.8

-0.2

+9.3

-1.4

-6.0

-0.8

3.97

+6.1

-13.6

+0.4

+ 16.2

-5.5

-3.4

-2.8

4.19

+ 13.9

-67.2

+ 1.5

+ 10.1

-3.7

-12.2

-5.8

*9. Prepare an activity-ratio diagram like that in Figure 1 1.2 for the soil solu-
tion described in Table 4.4. You may ignore the difference between activity
and concentration. Plot a point on the diagram representing (Al 3+ ) and
(Si (OH)"). What solid phase is predicted to control Al solubility?

10. The cation exchange reaction between Ca 2+ and Al 3+ in the O horizons of
Spodosols was found to be described well by the linear regression equation

log (Ca 2+ ) 3 /(Al 3+ ) 2
xl() S E cax 2 / E irx 3

-2.03 + 0.95 ± 0.06
(R 2 = 0.90)

where E is a charge fraction that serves as a model of the activity of an
exchangeable cation species on a soil adsorbent.

Ca/Al

a. Estimate the value of K ex for the cation exchange reaction. Which
cation is preferred by the soil adsorbent?

Soil Acidity 293

b. Given that Q = 3 mol c m -3 , prepare an exchange isotherm with the
charge fractions of Ca + used as plotting variables.

11. Manganese toxicity in acidic soils is associated with (Mn 2+ ) ~ 10 -3 ' 7
in the soil solution. Use relevant information in Table 6.1 to estimate the
pH value below which Mn toxicity should occur as pE ranges between 8
and 12.

12. Ammonium sulfate is applied to an acidic soil at the rate of 236 mg
(NH4)2S04 per kilogram of soil. Calculate the lime requirement for
neutralizing the total acidity expected if complete nitrification occurred,
without uptake of NH4, and the protons produced were entirely adsorbed
by the soil.

13. Calculate the lime requirement for the Inceptisols described in Problem
5 to increase their pH value from 3.5 to the point at which total acidity
equals zero. Take CEC = 160 mmol c kg - .

14. Apply Eq. 1 1.6 to calculate the lime requirement for soil humic acid car-
boxyl groups, as described by parameters given in Section 9.5, to increase
pH from pHjjis to the point at which TA ~ 0.

*15. Calculate the lime potential of the soil solution described in Table 4.4,
then estimate the corresponding ANC/CEC of the soil adsorbent using
Eq. 1 1.27. Neglect the difference between activity and concentration.

Special Topic 7: Measuring pH

As mentioned in Special Topic 5 (Chapter 6), Arnold Beckman developed an
instrument for measuring pH based on a glass electrode for detecting protons
in aqueous solution. This electrode comprises an outer membrane that adsorbs
protons and an inner solution containing a high concentration of Cl _ in
contact with a Ag/AgCl electrode. An electrode potential is created because of
proton concentration differences across the glass membrane, proton diffusion
processes within the membrane, and the oxidation half-reaction

Ag (s) + CT = AgCl (s) + e" log K = 3.75 (S7.1)

at the inner electrode. The pE value for the Ag/AgCl couple is fixed if the
activity of Cl _ is maintained constant (Section 6.1), hence the presence of
Cl _ in the inner solution. An electric potential difference between the glass
electrode and a reference electrode [usually the calomel electrode, at which
the reduction half-reaction

- Hg 2 Cl 2 (s) + e~ = Hg (I) + CI" log K = 4.13 (S7.2)

294 The Chemistry of Soils

takes place] then can be created by a difference in concentration of protons
between a soil solution and the inner solution of the glass electrode, provided
that a KCl "salt bridge" has been placed between the two electrodes to prevent
equilibration of the Cl _ concentration in the soil solution with that in the
reference electrode. The salt bridge is a porous plug intervening between the
soil solution and a saturated solution of KCl that bathes the calomel electrode.
Its purpose is to prevent mixing processes that would allow soil solution Cl _ to
equilibrate with the reference electrode and, therefore, contribute to the overall
electric potential difference that one wishes to attribute solely to protons.

Electric potential differences (E) in the glass— calomel electrode system are
modeled by an equation similar to Eq. 6.18:

E = A + Ej H In 10 pH = A + Ej + 0.05916 pH (S7.3)

where A is a constant parameter that depends on the redox reactions and ion
concentrations in the electrodes and Ej is the liquid junction potential created
by the variation in chemical composition that occurs across the salt bridge.
The value of Ej thus depends on the details of the steady-state charge transfer
through the liquid junction between a soil solution and the KCl salt bridge — a
necessary evil if the electrode system is to respond only to changes in proton
concentration. To measure proton activity, E is calibrated directly in terms
of the assigned pH values of buffer solutions. Therefore, by convention, only
relative values of pH can be measured:

„ „ % E (buffer) — E (soil solution)

pH soil solution = pH buffer + — (S7.4)

r * 0.05916

at 298 K, where the E values are in volts. [This convention differs very much
from that used for electron activity, which assigns pE = to the reduction of
the proton (third reaction in Table 6.1) at pH = 1 and Ph 2 = 1 atm, according
to Eq. 6.10.]

A principal difficulty in applying eqs. S7.3 and S7.4 to soil solutions is
uncertainty regarding the magnitude of Ej. Because soil solution composi-
tions differ greatly from those of pH buffers, the ions diffusing across the salt
bridge in the former differ from those in the latter, and the corresponding liq-
uid junction potentials can be quite different as well. It is virtually impossible
to know precisely how large this difference in Ej will be, because no method
exists for measuring or calculating Ej accurately. If the difference in Ej implicit
in Eq. S7.4 is indeed large and unknown, the pH value of the soil solution mea-
sured by a glass electrode would be of no chemical significance. This conclusion
is even stronger if one attempts to apply Eq. S7.4 to soil pastes or suspensions,
because then Ej is certainly very different in the soil system from what it is in
a standard buffer solution.

To see this issue in more detail, consider the situation in which the differ-
ence in E between a standard buffer solution and a soil solution arises solely

Soil Acidity 295

because of a difference in liquid junction potential, AEj, thus leading to an
apparent pH difference:

ApHj = AEj/59.16 (S7.5)

where AEj is in millivolts. Equation S7.5 is derived from combining Eqs. S7.3
and S7.4 under the assumed conditions. A difference in liquid junction poten-
tial equal to 10 mV (about 5% of the electrode potential corresponding to
the half-reactions in eqs. S7.1 and S7.2) leads to ApHj = 0.1, a rather large
systematic error. If, as a rule of thumb, pH measurements in soil solutions
are judged to be no more accurate than 0.05 log units, this degree of accuracy
would require liquid junction potential differences to be no larger than 3 mV.
(Of course, whether a pH value can be read from a pH meter to three decimal
places becomes irrelevant in this case!)

Compounding this problem is the difference in Ej between a soil solution
and a soil suspension caused by the presence of charged colloidal particles
in the latter. Suppose that, in fact, pH were the same in both systems. An
application of Eq. S7.3 then yields the expression

Eso - E Su = Ejso - Ejsu (S7.6)

where So refers to the soil solution and Su refers to the soil suspension.
Equation S7.6 describes the result of comparing the output of glass electrode
systems dipping respectively into a soil slurry and its supernatant solution,
with the slurry and solution in contact, such that equilibration of the protons
in the two has taken place. Thus, under equilibrium conditions, the electric
potential difference between the electrode pairs is determined solely by elec-
tric potential differences developed at two liquid junctions that involve KCl
salt bridges. The two E; values will differ because of the effect of soil col-
loids. The fact that this difference can develop is known as the suspension
effect. It is described in a classic article by Babcock and Overstreet [Babcock,
K. L., and R. Overstreet. (1953) On the use of calomel half cells to measure
Donnan potentials. Science 117:686.] and recently is discussed in great detail
by Oman et al. (Oman, S. E, M. F. Camoes, K. J. Powell, R. Rajagopalan, and
P. Spitzer. (2007) Guidelines for potentiometric measurements in suspensions.
Pure Appl. Chem. 79:67.], who point out that, in addition to anomalous liq-
uid junction potentials, nonunique electric potentials of the kind that often
plague electrochemical pE measurements (Section 6.3) also can occur for glass
electrodes inserted into soil suspensions.

Soil Salinity

12.1 Saline Soil Solutions

A soil is designated saline if the conductivity of its aqueous phase (EC e )
obtained by extraction from a saturated paste has a value more than 4 dS m .
(For a discussion of this measurement, see Methods of Soil Analysis, referenced
at the end of this chapter. The SI units of conductivity are defined in the
Appendix.) About a quarter of the agricultural soils worldwide are saline, but
values of EC e > 1 dS m are encountered typically in arid-zone soils, with a
climatic regime that produces evaporation rates that exceed precipitation rates
on an annual basis. Ions released into the soil solution by mineral weathering,
or introduced there by the intrusion of saline surface waters or groundwater,
tend to accumulate in the secondary minerals formed as the soils dry. These
secondary minerals include clay minerals (Section 2.3), carbonates and sul-
fates (Section 2.5), and chlorides. Because Na, K, Ca, and Mg are relatively
easily brought into solution — either as exchangeable cations displaced from
smectite and illite, or as structural cations dissolved from carbonates, sulfates,
and chlorides — it is this set of metals that contributes most to soil salinity. The
corresponding set of ligands that contributes then would be CO3 , SO4, and Cl.
Thus arid-zone soil solutions are essentially electrolyte solutions containing
chloride, sulfate, and carbonate salts of Group IA and IIA metals.

According to Eq. 4.23, a conductivity of 4 dS m _1 corresponds to an ionic
strength of 58 molm" 3 (i.e., log I = 1.159 + 1.009 log 4 = 1.77). This salinity
is 10% of that in seawater, high enough in an agricultural context that only
crops that are relatively salt tolerant can withstand it. Moderately salt-sensitive

296

Soil Salinity 297

crops are affected when the conductivity of a soil extract approaches 2 dS m ,
corresponding to an estimated ionic strength of 29 mol m . Salt-sensitive
crops are affected at 1 dS m _1 (I = 14 mol m -3 ). Thus, with respect to
salinity tolerance, a soil can be saline at any ionic strength greater than 15
mol m if the plants growing in it are stressed. The visual evidence of this
is a reduction in crop growth and yield caused by a diversion of energy from
normal physiological processes to those involved in the acquisition of water
under osmotic stress.

The chemical speciation of a saline soil solution can be calculated as
described in sections 4.3 and 4.4. Total concentration data and the percent-
age speciation that are representative of the saturation extract of an irrigated
Aridisol are listed in Table 12.1. Notable in the table are the dominance of sol-
uble Ca over Mg; the relatively complicated speciation of Ca, Mg, HC07, SO4,
and PO4; and the high free-ion percentages for Na, K, Cl, and NO3. (Note that
organic complexes are unimportant for the metal cations considered.) Neutral
sulfate complexes reduce the contribution of SO4 to the ionic strength — and,
therefore, the conductivity — by more than one fourth. The computed ionic
strength of the soil solution in Table 12.1 is 23 mol m -3 , which corresponds
to an estimated conductivity of 1.6 dS m _1 , which is high enough to affect
salt- sensitive crops.

The alkalinity of a saline soil solution can be defined by Eq. 11.3, with
neglect of organic and Al(III) species, of course, but with inclusion ofB (OH) ^ ,
leading to the expression

Alkalinity = [HCO~] + 2 [CO3"] + [H 2 PO~] + 2 [HP07] + 3 [PO 3- ]
+ [B(OH)7] + [OH"] - [H+] (12.1)

Table 12.1

Composition and speciation of an Aridisol soil solution (pH 8.0).

Constituent C T Percentage speciation

(mol m~ 3 )

5.9

Ca 2 + (79%), CaSO° (17%), CaHCO+ (2%)

1.3

Mg 2+ (83%),SO° (14%),MgHCO+ (1%)

1.9

Na+ (99%)

1.0

K+ (99%),KS07 (1%)

co 3

3.0

HC07 (92%),H 2 CO° (2%),CaHCO+ (4%),
CaCO§ (2%)

SO4

4.4

SO 2 " (72%),CaSO° (23%),MgSO° (4%)

5.0

Cl" (99%)

no 3

0.28

NOT (99%)

po 4

0.065

HPO^" (46%),CaHPO° (30%),MgHPO^ (9%),
H 2 PC"7 (5%),CaP07 (9%)

0.038

B(OH)° (3%),B(OH)7 (6%)

298 The Chemistry of Soils

for a soil solution like that described in Table 12.1. (As mentioned in Section
11.3, the concentrations of metal complexes of the anions on the right side
of Eq. 12.1 can be included readily.) In the example of Table 12.1, the alka-
linity equals 2.8 mol m -3 , with 99% derived from bicarbonate. Bicarbonate
alkalinity ranging from 1 to 4 mol m is common in saline soils.

The pH value of a saline soil solution with an alkalinity derived from
bicarbonate is governed by Eq. 1 1.2:

pH = 7.8 + log (HCO3-) - log P C o 2 (12.2)

If the Davies equation (Eq. 4.24) is used to calculate the activity coefficient of
HCO^~, and if the Marion-Babcock equation (Eq. 4.23) is used to relate ionic
strength to conductivity, then Eq. 12.2 takes the form

where

pH = 7.8 + A(k) + log [HCO3-] - log P C o 2 (12.3)

0.12V*:

A(k) ss -0.512

1 + 0.12Vi<

■ 0.0043k

(12.4)

is a very small correction for ionic strength effects [A(k) < — 0.1 for k < 4
dS m -1 ]. Equation 12.3 shows that soil solution pH is determined by the
bicarbonate alkalinity and the CC>2(g) pressure in atmospheres. Conversely, the
CC>2(g) pressure at equilibrium can be calculated with Eq. 12.3 from measured
pH and alkalinity values. Given Pco 2 = 10 atm, the atmospheric value,
the range of [HCOj - ] quoted earlier leads to pH values in the range 8 to 9.
For the soil solution of Table 12.1, pH = 8.0, [HCO3"] = 0.00276 mol dm -3 ,
and a C02(g) pressure of 10 -2 ' 9 atm is calculated. Note that Eq. 12.3 predicts
increasing soil solution pH with either increasing bicarbonate alkalinity or
decreasing CO2 (g) pressure. This relationship has often been observed in arid-
zone soils.

12.2 Cation Exchange and Colloidal Phenomena

Exchange reactions among the cations Na + , Ca , and Mg + are of great
importance in arid-zone soils. These reactions, in the convention of Eq. 9.14b,
can be expressed as

2 NaX(s) + Ca 2+ = CaX 2 (s) + 2Na+ (12.5a)

2 NaX(s) + Mg 2+ = MgX 2 (s) + 2Na+ (12.5b)

MgX 2 (s) + Ca 2+ = CaX 2 (s) + Mg 2+ (12.5c)

where X represents 1 mol intrinsic negative surface charge. (Note that any one
of these reactions can be obtained by combining the other two.) Exchange

Soil Salinity 299

isotherms based on the reactions in Eq. 12.5 are shown in Figure 9.2 for an
Aridisol. They indicate, as observed typically for arid-zone soils, that Ca and
Mg are preferred over Na, and that Ca is preferred slightly over Mg by the
soil adsorbent. A conditional exchange equilibrium constant for the reaction
in Eq. 12.5a is presented in Eq. 9.18, and analogous expressions apply to the
reactions in Eqs. 12.5b and 12.5c. Although these Vanselow model selectivity
coefficients do vary with adsorbate composition, the variability is small enough

Na/Ca

to neglect to a first approximation. For example, if K y ~ 16, then Eq. 9.20
predicts Ec a ~ 0.8 when Ec a ~ 0.05 [along with Q = 0.05 mol c dm -3
(A = 0.037)], which agrees with the exchange isotherm for Ca in Figure 9.2.

By the same process used to derive Eq. 9.20 from Eq. 9.18, one can rewrite
Eq. 9.18 in the form

K N a/ Ca = r ^J/ L ^ J (l _ Ey (126)

4b Na

where T = y-^Jyca and y is a single-ion activity coefficient (Eq. 4.24).
Equation 12.6 contains two important chemical variables. The expression

SAR=10 3 / 2 [Na+]/[Ca 2 +] 1/2 (12.7)

defines the sodium adsorption ratio (SAR) and 100 E^a = ESP defines the
exchangeable sodium percentage (ESP). With these two definitions, Eq. 12.7
becomes the expression

< a/Ca = 2.5 r/^) [1 - (ESP/100) 2 ]

(12.8)

Given a value for K y , Eq. 12.8 provides a unique relationship between
ESP and SAR. This relationship is essentially a linear one for SAR <
20 mol ' m _3 ' 2 andKy > 1. The variable defined by Eq. 12.7 is equivalent
to using SI units of moles per cubic meter instead of moles per liter:

SAR = c Na /Vc^ (12.9)

where c is concentration in SI units (see the Appendix). Because direct mea-
surements of the free-ion concentrations of Na + and Ca + are not common
in field work, SAR in Eq. 12.9 usually is replaced by the variable SAR p :

SARp = Nat/v^CaT (12.10)

where the subscript p indicates the practical SAR, and total concentrations
in SI units are indicated on the right side. This variable is typically smaller
than SAR because of greater soluble complex formation by Ca + than Na + .
(For example, it is 10% smaller for the soil solution speciated in Table 12.1).
Statistical analyses of the SAR p -SAR relationship in soil saturation extracts

300 The Chemistry of Soils

indicate that SAR p is about 12% smaller than SAR, on average. This small
difference and the deviation of Eq. 12.8 from a 1:1 line are often neglected in
applications to irrigation water quality evaluation, with the result that Eq. 12.8
simplifies to the expression

ESP ss SAR p (SARp < 30) (12.11)

Equation 12.11 has long been used in field studies of ESP. Given the several
approximations leading to it, along with its intended application to evaluate

• ■ • i-i i- -i T ,Na/Ca T ^Na/Mg r

irrigation water quality, the expedient assumption that K y ~ K v tor

Na — > Mg exchange also is made, such that SAR p can be generalized to

SARp = Na T /(Ca T + Mg T ) 1/2 (12.12)

and incorporated into Eq. 12.11. Although the chain of assumptions link-
ing Eq. 12.11 to Eq. 12.6 via Eq. 12.12 is somewhat tenuous and long, it is
well defined enough to make the conceptual basis of the ESP-SAR p relation
apparent.

The important differences between monovalent and bivalent cations in
respect to the stability of colloidal suspensions are discussed in Chapter 10 (see
Eq. 10.17 and Problem 6). Laboratory studies of the stability ratio for suspen-
sions of soil colloids based on turbidity measurements (see Problems 8 and 9 in
Chapter 10) suggest that stable suspensions are the rule if ESP > 15%. Studies
of the permeability characteristics and aggregate structures in arid-zone soils
have substantiated this effect of adsorbed Na + , leading to the designation sodic
for a soil in which the ESP value is larger than about 15. In these soils, if the
ionic strength is low, colloids will tend to disperse in the soil solution, and a
reduction in permeability will occur because of aggregate failure and swelling
phenomena (Section 10.2). However, the dispersive effect of exchangeable
Na + will be observed only if the electrolyte concentration is less than that
required to maintain the integrity of soil aggregate structures. The upper limit
of this concentration is the ccc (Section 10.3), but the electrolyte concentration
at which a noticeable (say, 15%) decline in soil permeability occurs may be
lower than the ccc. Regardless of the exact value of this threshold electrolyte
concentration, the key point is that soil salinity tends to counteract the effect of
exchangeable sodium on soil aggregate structure.

Equation 10.17, which quantifies the Schulze-Hardy Rule (Section 10.3),
implies that Ca-saturated colloids flocculate at electrolyte concentrations
about 60 times smaller than those required to flocculate Na-saturated col-
loids. Thus ESP (or SAR) must be related to colloidal stability and, therefore,
aggregate failure. This kind of relationship has been found in a large number of
experiments with soils. Examples are shown in figures 12.1 and 12.2. They are
termed Quirk-Scho field diagrams, graphs of the electrolyte concentration (or
conductivity) below which significant deterioration in aggregate soil structure
should occur (as measured, for example, by a 15% loss of permeability), plot-
ted against the SAR p value above which the same deterioration in soil structure

Soil Salinity 301

4 i-

LLI

Good soil
structure

Poor soil
structure

SAR

10
pw (mol m )

Figure 12.1. A Quirk— Schofield diagram for California soils based on the properties
of water applied for irrigation (conductivity vs. practical sodium adsorption ratio).
Note the large error bars to allow for effects of pH and soil variability. Data from
Shainberg, I., and J. Letey (1984) Response of soils to sodic and saline conditions.
Hilgardia 52(2): 1-55.

•

Poor soil structure

C\i

"o
E

30
20

- •

• •

•
• •

• •

....

Good soil structure

10 20 30 4(
Q w (mol c m- 3 )

Figure 12.2. A Quirk-Schofield diagram for irrigated soils based on the properties
of irrigation water (practical SAR vs. the threshold electrolyte charge concentration
causing a 15% reduction in soil permeability). Note that the graph has coordinate axes
reversed from those in Figure 12.1. Data from Quirk, J.R (2001) The significance of
the threshold and turbidity concentrations in relation to sodicity and microstructure.
Aust. J. Soil Res. 39:1185-1217.

302 The Chemistry of Soils

should take place. Figures 12.1 and 12.2 are Quirk— Schofield diagrams based
on experiments relating mainly to California soils. A "window," allowing for
variability among soils, separates regions of expected good and poor soil struc-
ture as expressed by permeability characteristics. Note that any soil for which
the SARp electrolyte concentration combination falls into the poor soil struc-
ture region could be termed sodic, insofar as soil permeability is concerned.
An SARp value of 15 would lead to poor soil structure only if the electrolyte
concentration dropped below about 10 mol m (EC < 1.5 dS m _ ). On the
other hand, an apparently low SAR p value of 3.0 would still lead to poor soil
structure if the electrolyte concentration dropped below about 2 mol m -3
(EC < 0.2 dS m _ ). A saline soil as defined conventionally should not have
poor structure unless the SAR p value rises well above 30.

As discussed in Section 10.4, the stability ratio for a colloidal suspension
is also affected by pH and strongly adsorbing ions (see Table 10.1). Laboratory
studies of colloidal suspensions from arid-zone soils indicate that pH effects
are relatively minor at pH > 6, but that polymeric ions (e.g., Al-hydroxy
polymers or humus) exert strong effects, with dissolved humus enhancing
stability considerably (see Problem 12 in Chapter 10).

12.3 Mineral Weathering

Soils in arid regions are often at the early stage of the Jackson— Sherman weath-
ering sequence (Table 1.7) and, therefore, they contain silicate, carbonate, and
sulfate minerals that are relatively susceptible to dissolution reactions in per-
colating water. The composition and structures of these minerals are described
in sections 2.2 and 2.5. Their dissolution reactions are discussed in sections
5.1 and 5.5. (See also Problem 15 in Chapter 1; Problem 11 in Chapter 2;
and problems 3, 4, 6, and 8 in Chapter 5.) Laboratory studies have shown
that these reactions may add 3 to 5 mol c m in charge concentration to per-
colating waters, with most of the addition coming from Ca, Mg, and HCO3
under alkaline soil conditions (see Table 12.1). A dissolution reaction of the
easily weatherable silicate mineral anorthite, which can produce this effect, is
illustrated in Eq. 2.8 and discussed further in Problem 6 of Chapter 5.

Soil mineral weathering that increases the salinity of the soil solution
and enriches it in Ca and Mg has important implications for the colloidal
phenomena discussed in Section 12.2. If water entering a soil has a very low
electrolyte concentration (e.g., rainwater or irrigation water diverted from
pristine surface waters), a very small SAR pw in the water would be sufficient to
cause problems with soil structure and permeability (figs. 12.1 and 12.2). For
example, SAR pw values as low as 3.0 can be deleterious to soil structure if the
applied water EC W is around 0.5 dS m . On the other hand, infiltrating water
that causes soil minerals to dissolve and increase the conductivity of the soil
solution to near 1.0 dS m _1 would make only SAR p values > 5.0 of concern.
Moreover, if most of the increase in electrolyte concentration came from Ca 2+

Soil Salinity 303

and Mg , then the SAR p value would actually drop in the equilibrated soil
solution (Eq. 12.12), further diminishing the chance of adverse soil structure
effects. The conclusion to be drawn is that soils containing easily weatherable
minerals will be less sensitive to percolating low-salinity waters than those that
are depleted of easily weatherable minerals.

Increasing salinity tends to enhance the solubility of weatherable miner-
als. This effect can be predicted on the basis of the ionic strength dependence
of single-ion activity coefficients (Eq. 4.24). Consider, for example, the min-
eral gypsum (CaS04 • 2H2O), with the solubility product constant defined in
Eq. 5.8:

K so = (Ca 2+ ) (SO 2- ) = 2.4 x 10" 5 (12.13)

The solubility of gypsum is related to the concentration of Ca 2+ (see Problem 3
in Chapter 5) and, therefore, to the conditional solubility product, K soc :

K soc = [Ca 2+ ] [SO 2 "] = K so /y C ayso 4 (12-14)

where the y's are single-ion activity coefficients. It follows from Eqs. 4.24 and

log K soc = log K so + 4.096

i + vT

0.31

(12.15)

where I is ionic strength in moles per cubic decimeter. This equation shows
that the conditional solubility product will increase with ionic strength, as long
as the term in the square root of I exceeds 0.3 I (i.e., as long as I < 2moldm ).
For example, experimental studies of the enhancement of gypsum solubility
in NaCl solutions show that when the concentration of NaCl increases up to
0.5 moldm , the total concentration of Cain equilibrium with gypsum more
than doubles.

The weathering reactions of calcite (CaCC^) are of great importance in
arid-zone soils. As discussed in Section 5.1, the dissolution of this mineral
far from equilibrium is surface controlled and, therefore, follows a zero-
order kinetics expression (Eq. 5.2, with Ca 2+ replacing A). The net rate of
precipitation-dissolution near equilibrium can be expressed analogously to
Eq. 5.16 (see Problem 4 in Chapter 5):

d rca 2 +i

-L- l = kpK soc (1 - £2) (12.16)

where k p is a rate coefficient for precipitation that depends on pH and specific
surface area and K so = 3.3 x 10 -9 is the solubility product constant for
well- crystallized calcite undergoing the dissolution reaction

CaC0 3 (s) = Ca 2+ + C0 2 ~ (12.17)

(Ca 2+ ) (CO 2- ) is the IAP, and Q, = (Ca 2+ ) (CO 2- ) /K so . Equation 12.16
describes the net rate of precipitation of calcite if Q, > 1 (supersaturation).

304 The Chemistry of Soils

For that case, if £2 < 10 and pH > 8, k p K soc ~ 2.5 x 10 -9 mol L _1 s _1 . For
an initial Ca + concentration of, say, 0.001 mol dm , Table 4.2 indicates a
half-life on the order of hours (ti/2 = [Ca 2+ ] /2k p K so £2).

Another useful rate expression analogous to that in Eq. 5.16 is obtained
by transforming the IAP according to the calcite dissolution reaction in
Eq. 5.32:

CaC0 3 (s) + H+ = Ca 2+ + HCO~ (12.18)

Given the equilibrium constant for the bicarbonate formation reaction

h + + co 2 ~ = hco~ K 2 = 10 10 - 329 (12.19)

where K 2 = (HCO^) / (H+) (CO 2- ), one can rewrite Eq. 5.16 in the
alternative form

d [Ca 2+ 1
L dt J = k p K soc [l - (Ca 2+ ) (HCO3-) /K 2 K so (H+)] (12.20)

The relationship (H + ) = 10 _p and the Langelier Index, pH-pH s , where pH s
is defined by the equation

(Ca 2+ ) (HCO3") /K 2 K so = 10" pH s (12.21)

may be used to transform Eq. 12.20 into the simpler expression

^-1 = k p K soc [1 - 10P H "P H s] (12.22)

Equation 12.22 yields estimates of the rate of calcite precipitation or dissolu-
tion based on the Langlier index. To illustrate this relationship, consider Ca +
and HCOj" activities based on the chemical speciation of the soil solution
described in Table 12.1: (Ca 2+ ) R» 2.59 x 10- 3 ,HCO~ ss 2.38 x 10" 3 , and
pH s = 7.02. It follows from Eq. 12.22 that, at pH 8, the Langlier index equals
0.98 and the soil solution is supersaturated with respect to calcite (i.e., the right
side of Eq. 12.22 is negative). The same conclusion is reached by calculating
Q. directly for the soil solution:

_ (Ca 2+ ) (CO 2- ) _ 2.59 x 10" 3 x 1.19 x 10" 5 _
K so 3.3 x 10" 9

Because Q. > 1, the soil solution is supersaturated with respect to well-
crystallized calcite.

The value of £2 just calculated leads to an IAP ~ 10 -8 for calcite in the
soil solution described in Table 12.1. This high value in fact has been observed
consistently in a large number of investigations of calcite solubility in arid-
zone soils. The cause of ubiquitous supersaturation is not analytical error,
crystalline disorder (Section 5.5), or Mg substitution for Ca (Section 2.5), but

Soil Salinity 305

most likely is a kinetics-based mechanism relating to Eq. 12.16 (see Problem
6 in Chapter 5). One possibility is a reduction in k p produced by the adsorp-
tion of soluble humus on the surfaces of calcite particles. Laboratory research
has shown that calcite precipitation is inhibited greatly by adsorbed fulvic
acid, which can reduce k p by two orders of magnitude. Another possibility is
sustained production of bicarbonate alkalinity through the oxidation of soil
humus. Arid-zone soils incubated with plant litter at ambient Pco 2 readily
produce HCO^~ that increases in concentration as the plant materials decom-
pose. High bicarbonate concentrations may be sustained under steady-state
conditions, leading to a persistently high IAP for calcite.

12.4 Boron Chemistry

Boron is a trace element in soils (Table 1.1) that occurs typically as a
coprecipitated element in secondary metal oxides, clay minerals, and mica,
or as a substituent in humus (tables 1.4 and 1.5). Besides its occurrence
as a separate solid phase in tourmaline, a number of Na, K, Ca, and Mg
borates have been identified in saline geological environments. Among them
are borax [Na 2 B 4 5 (OH) 4 -8H 2 0], nobleite [CaB 6 9 (OH) 2 -3H 2 0], iny-
oite [CaB 3 03(OH)5-4H 2 0], colemanite [CaB 3 04(OH)3-H 2 0], and inderite
[MgB303(OH)5-5H 2 0]. Dissolution equilibrium constants and a representa-
tive value for the activity of Na + , Ca , or Mg + in arid-zone soil solutions
(Table 12.1) lead to the conclusion that borate minerals would support very
high B solubilities in the soil solution. For example, to achieve the concen-
tration of B(OH)j indicated in Table 12.1 (35 mmol m ), only very small
amounts of these minerals would have to be present in soil — amounts that
should be easily lost by normal leaching. The dissociation reaction

B(OH)° + H 2 (I) = B(OH)~ + H+ (12.23)

has an equilibrium constant equal to 5.8 x 10 (logiC = 9.23). Therefore,
the B(OH)^" species will not be significant in soil solutions [i.e., will not be
equal to the concentration of B(OH)j] until the pH value approaches 9. This
is true also for complexes like CaB(OH)^~ and MgB(OH)^~, which account for
less than 0.5% of the boron species in the soil solution described in Table 12.1.
Boron concentrations in arid-zone soil solutions can range up to
2 molm -3 , depending on the mineralogy of soil parent material or the com-
position of groundwater. Sensitive crop plants are affected by concentrations
greater than 0.046 mol B m , and almost all crops will be affected at concen-
trations greater than 0.5 mol m -3 . These threshold concentrations translate to
irrigation water concentrations of 65 and 277 mmol m -3 respectively. Leach-
ing experiments indicate that high B concentrations cannot be reduced easily
by percolating fresh water (>3-5 years required). The rate of B removal is
much less than that for chloride, and a resurgence of B concentration can occur
after it has been reduced by extensive leaching. This behavior suggests not only

306 The Chemistry of Soils

that soil B is released slowly from minerals in which it is a trace component
(Tables 1.4 and 1.5), but also that it adsorbs strongly onto soil particle surfaces.
An adsorption envelope for B(OH)^" on a calcareous Entisol is shown
in Figure 8.5 (see also Fig. 7.9). The resonance feature in it results from an
interplay between adsorptive and adsorbent charge, as discussed in Section
8.4. The similarity in adsorption envelopes between F _ and B(OH)^" in soils
(cf. figs. 8.4 and 8.5), as well as studies of B adsorption by specimen miner-
als, suggest that the principal adsorption mechanism is ligand exchange with
surface hydroxyls (Eq. 8.25):

=SOH(s) + B(OH)^ = =SOB(OH)~ + H+ (12.24)

Support for this mechanism has come from infrared spectroscopy and from
modeling studies wherein the constant capacitance model has been applied
to describe adsorption envelopes like that in Figure 8.5. These studies and
experimental investigations with specimen minerals indicate that surface OH
groups are the main reactive sites for B adsorption. The low leachability of
adsorbed boron then derives from the strong inner-sphere surface complex
formed in conjunction with the reaction in Eq. 12.24.

The constant capacitance model describes specific borate adsorption
based on Eq. 12.24 and two surface acid— base reactions like that depicted
in Eq. 8.25a and the corresponding proton dissociation reaction:

=SOH (s) + H+ = =SOH+ (s) (12.25a)

=SOH(s) = =SO"(s) +H+ (12.25b)

These reactions govern adsorbent surface charge, whereas Eq. 12.23 governs
adsorptive charge, with the connection between them mediated by the reac-
tion in Eq. 12.24. According to the model, the equilibrium constants for the
reactions in eqs. 12.24 and 12.25 are

|=SOH+l
K+ = [=SOH] [H+] 6XP ( F °P /asC/RT ) (12 - 26a)

[=SO-l [H+l
K_ = L [=S q^ «p (-Fop/a s C/RT) (12.26b)

|=SOB(OH)"l [H+l

K b = r JL „-, J exp (-Fo- p /a s C/RT) (12.26c)

[=SOH] [B(OH)°] FV p/ '

where F is the Faraday constant (coulombs per mole of charge, C mol~ ), R is
the molar gas constant (joules per mole per kelvin, J mol - K _1 ), and T is the
absolute temperature (kelvin, K).

Soil Salinity 307

The exponential factors in Eq. 12.26 contain the net particle charge
(Section 7.3)

a p = j [=SOH+] - [sSO-] - [=SB(OH)7] ]/c s (12.27)

where c s is a solids concentration (e.g., Eq. 3.7), which is then divided by
the product of specific surface area and a capacitance density (C) with a
default value of 1.06 F m (the same as coulomb-squared per joule per
square meter, C 2 J -1 m -2 ), as determined through a broad variety of appli-
cations of the model to specific adsorption data. These factors are model
expressions for the activity coefficients of the surface species that appear in the
numerator in each equation for an equilibrium constant. In this sense, the
model is a generalization of approaches like that in the biotic ligand model
(Section 9.4), for which equilibrium constants contain only concentrations
(Eq. 9.22).

Besides the universal parameter F/RT (=38.917 C J" 1 at 298 K), the
valence of the surface species (e.g., +1 for =SOH2 ) and the particle charge
enter into an activity coefficient. When these two parameters have the same
sign, the exponential factor is more than one and the surface species concen-
tration is reduced relative to its value at the p.z.c. [i.e., when a p = (Section
10.4)]. When the two parameters are of opposite sign, the exponential factor
is less than one and the reverse situation occurs. Thus, the constant capaci-
tance model activity coefficient represents the effect of coulomb interactions
between the adsorptive and adsorbent analogously to the way a single-ion
activity coefficient does for aqueous species (Section 4.5). The capacitance
density C modulates this effect, but, because of its unit value, acts mainly as a
conversion factor between the units of er p /a s and those of F/RT so as to render
the exponent in the activity coefficient expression dimensionless. Applica-
tion of the model to a large number of soils has led to regression equations
that can be used to estimate the three equilibrium constants in Eq. 12.26
from just four soil properties: specific surface area, Al oxide content, and the
content of both organic and inorganic C. The empirical coefficients in these
equations are

log K+ = 7.85 - 0.102 In (f oc ) - 0.198 In (f ioc ) - 0.622 In (Al) (12.28a)

log K_ = -11.97 + 0.302 In (f oc ) + 0.584 In (f ioc ) + 0.302 In (Al)

(12.28b)

log K B = -9.14 - 0.375 In (a s ) + 0.167 In (f oc )

+ 0.111 In (f ioc ) + 0.466 ln(Al) (12.28c)

where a s is in square meters per gram, whereas f oc , fioo and Al are in grams
per kilogram. Once the model equilibrium constants have been estimated,
chemical speciation calculations as described in Section 4.4 can be performed
with the exponential factors in Eq. 12.26 treated like aqueous species activity

308 The Chemistry of Soils

coefficients and er p in Eq. 12.27 playing a role analogous to ionic strength.
The typical ranges of values of the log equilibrium constants are approxi-
mately: 7.3 < logK + < 9.4,-12.6 < logK_ < -10.5, and -8.9 < log
K B < -7.3.

12.5 Irrigation Water Quality

The sustainable use of a water resource for the irrigation of agricultural land
requires that there be no adverse effects of the applied water in the soil environ-
ment. From the perspective of soil chemistry, all irrigation waters are mixed
electrolyte solutions. Their chemical composition, which reflects their source
and postwithdrawal treatment, may not be compatible with the suite of com-
pounds and weathering processes that exist in the soils to which they are
applied. Adding to this the salt- concentrating effects of evaporation, crop
extraction of water, and fertilizer amendments, one readily sees the possibility
that irrigated soils can become saline or sodic without careful management.

The chemical properties of irrigation water that must be identified and
controlled to maintain the water suitable for agricultural use are termed irri-
gation water quality criteria. The numerical interpretation of the water quality
criteria to achieve goals in irrigation water quality management leads to water
quality standards. These two distinct aspects of irrigation water quality are
determined in the first case by the results of field and laboratory research and
in the second by research data combined with the collective experience of
extension scientists, farm advisers, and growers.

The three principal water quality-related problems in irrigated agriculture
are salinity hazard, sodicity hazard, and toxicity hazard. Irrigation water quality

Table 12.2

Irrigation water quality standards to control soil salinity and sodicity
hazards. 3

Restriction on water use

None

Slight to moderate

Severe

Salinity hazard EC W (dS m )

< 0.75

0.75-3.0

> 3.0

Sodicity hazard SAR pw range
(mol 1 / 2 rrT 3 / 2 )

EC^dSm" 1 )

0-3

>0.7

0.7-0.2

<0.2

3-6

>1.2

1.2-0.3

<0.3

6-12

>1.9

1.9-0.5

<0.5

12-20

>2.9

2.9-1.3

<1.3

"Adapted from Ayers, R. S., and D. W. Wescot. (1985) Water quality for agriculture. FAO
irrigation and drainage paper no. 29, rev. 1. FAO, Rome.

SAR pw denned in Eq. 12. 12 for total concentrations in irrigation water. The first three ranges
correspond to sodicity hazard criteria of "none", "moderate", and "severe" respectively.

Soil Salinity 309

Table 12.3

The factor X(LF) in Eq. 12.30. a

LF X(LF) LF X(LF)

0.05

3.2

0.30

1.0

0.10

2.1

0.40

0.9

0.15

1.6

0.50

0.8

0.20

1.3

0.60

0.7

0.25

1.2

0.70

0.6

"Adapted from Ayers, R. S., and D. W. Wescot. (1985) Water
quality for agriculture. FAO irrigation and drainage paper
no. 29, rev. 1 . FAO, Rome.

standards to control salinity hazard are listed in Table 12.2. They are designated
preferentially by three classes of conductivity (EC W ), measured in decisiemens
per meter. These classes correspond approximately to groupings of agricul-
tural crops into sensitive, relatively sensitive, and relatively tolerant categories
respectively. Thus, for example, sensitive crops require EC W < 0.75 dS m _1 ,
and only relatively tolerant crops can withstand EC W > 3 dS m with-
out significant yield reduction. According to Eq. 4.22, the three EC W ranges
in Table 12.3 are equivalent to the ionic strength ranges: I < 11 molm -3 ,
11 < I < 44 mol m -3 , and I > 44 mol m -3 .

The definition of a saline soil refers to the conductivity of the soil sat-
uration extract (EC e ), not to that of applied water. Even though EC W is
recommended to be < 3 dS m _1 , the validity of this restriction depends
on knowing the relationship between EC W and EC e in the root zone. This
relationship continues to be the subject of much research in the chemistry
of soil salinity, because many complicated factors enter into it, even in the
absence of external effects from rainwater and shallow groundwater. As a
rule of thumb, the steady-state value of EC e that results from irrigation with
water of conductivity EC W is estimated from a knowledge of the leaching
fraction (LF) of the applied water. The leaching fraction is defined by the
equation

volume of water leached below root zone

LF= : (12.29)

volume of water applied

Typically, LF is in the range 0.05 to 0.20, meaning that 5% to 20% of the
water applied leaches below the root zone whereas 80% to 95% is used in
evapotranspiration. With the value of LF known, the average value of EC e in
the root zone is estimated as

EC e = X(LF)EC w (12.30)

where X(LF) is a function with a dependence on LF that has been worked out
on the basis of experience with typical irrigated, cropped soils. The function

310 The Chemistry of Soils

X(LF) is given in numerical form in Table 12.3. As an example of its use, if
water with EC W = 1.2 dS m is applied and LF = 0.25, then EC e is predicted
to be 1.44 dS m _1 , on average, in the root zone. Note that LF > 0.3 results in
EC e < EC W , and that LF < 0.1 will produce a saline soil if water with EC W >
2 dS m is applied.

Irrigation water quality standards to control sodicity hazard are also listed
in Table 12.2. They reflect the interplay between electrolyte concentration and
exchangeable cation composition discussed in Section 12.2. Thus, for example,
if SAR pw is in the range of 3 to 6 mol ' m ' and EC W is > 1.2 dS m ,
the development of poor soil structure from exchangeable sodium is unlikely
because the electrolyte concentration in the applied water is large enough to
maintain the integrity of soil aggregates. It is instructive to compare Table 12.2
with figures 12.1 and 12.2.

The cation exchange relationship on which the use of SAR pw is based
refers to SAR in the soil solution, not in applied irrigation water. Like EC W and
EC e , the relationship between SAR pw and the soil solution SAR is the subject
of current research. The conversion of SAR pw to an SAR W value involving free-
cation concentrations can be made with the help of the "12% rule of thumb"
mentioned in Section 12.2. More serious, usually, is the need to account for
calcite precipitation or dissolution as the irrigation water percolates into soil
under the influence of ambient C02(g) pressures. For this purpose, the Suarez
adjusted sodium adsorption ratio may be used to estimate ESP with Eq. 12.8.
This parameter, denoted ad] RNa, is defined by the equation

adj RNa = c Naw / [c Mgw + c^J (12.31)

where c is a free-cation concentration in moles per cubic meter, and c c ^ is
the concentration of Ca 2+ in a soil solution having the same activity ratio
(HCO^j / (Ca + J as the irrigation water when it is in equilibrium with calcite
at a soil value of Pco 2 ( m atmospheres).

The relationship between c c ^ and the [HCO^~] / [Ca 2+ ] ratio in irriga-
tion water, necessary to apply Eq. 12.31, can be derived from the relationship
between the relative saturation and the Langlier index implicit in Eq. 12.22:

£2 W = ioP H w-P R s (12.32)

where pH w is now the pH value of the irrigation water. Equation 12.2 can be
combined with Eq. 12.21 to derive from Eq. 12.32 the alternative expression:

£2 W = (Ca 2+ ) w (HC0 3 -)^ /10 2 - 5 K so P C o 2 (12.33)

where the numerical factor is equal to K2/IO 7,8 . The denominator inEq. 12.33

'eq V 3 /eq'

is equal to (Ca + ) (HCO3 ) , as can be seen by setting £2 W = 1.0 in the

Soil Salinity 311

equation and changing "w" to "eq" for that case. It follows that

(Ca 2+ ) w (HC0 3 -)i

(Ca 2 +) -

" (HCO-)>

'eq

which can be transformed to the equation

v3 ,„ ?+ x 3

( Ca2+ )e q =( Ca2+ )w/^w (12.34)

on multiplying by (Ca 2+ ) 2 on both sides, then multiplying by
[(Ca + ) w /(Ca 2+ ) w ] 2 on the right side only using the condition
(HCO^~)eq/(Ca 2+ )eq = (HCO^~) w /(Ca 2+ ) w assumed by hypothesis. The
substitution of Eq. 12.33 into Eq. 12.34 yields the expression desired:

^-^ A P rn ./3 (12.35)

[(HCO-) w /(Ca 2 + ) w ] 2 | C ^

Equation 12.35 can be used to calculate c c ^ (which differs by a factor of 10 3
from [Ca + ] e q) after values of Pco 2 > [HCO^~]/[Ca + ], the activity coefficients
of Ca + and HCO^~ and K so have been chosen. The value of K so at 25 °C
ranges from 3.3 x 10 to 4.1 x 10 , depending on the crystallinity of calcite
(Section 5.5). Alternatively, the IAP value of 10 -8 can be used as a surrogate for
K so in soils (Section 12.3). The single-ion activity coefficients can be estimated
using a selected EC W along with eqs. 4.23 and 4.24. For example, if EC W = 1
dS m , then xhco 3 = 0.886 L mol - and yea = 0.616 L mol . Suppose
that [HCO~]/[Ca 2+ ] = 2. Then, if K so = 10" 8 and P C o 2 = 10" 3 (Section
5.5), Eq. 12.35 yields Cq = 1.1 mol m _ . This prediction can be introduced
into Eqs. 12.31 and 12.8 to estimate a soil ESP value.

For Further Reading

Goldberg, S. (1993) Chemistry and mineralogy of boron in soils, pp. 3-44. In:
U. C. Gupta (ed.), Boron and its role in crop production. CRC Press, Boca
Raton, FL. An advanced exposition on the soil chemistry of boron that
amplifies the discussion in Section 12.4.

Karen, R. (2000) Salinity. Levy, G. J. (2000) Sodicity, pp G-3 to G-63. In:
M. E. Sumner (ed.), Handbook of soil science. CRC Press, Boca Raton,
FL. These two chapters provide a sound introduction to the chemistry of
arid-zone soils.

Levy, R. (1984) Chemistry of irrigated soils. Van Nostrand, New York. Collected
classic articles on a classic soil chemistry problem.

Mays, D. C. (2007) Using the Quirk-Schofield diagram to explain environ-
mental colloid dispersion phenomena. /. Nat. Resour. Life Sci. Educ.

312 The Chemistry of Soils

36:45. A useful introduction to the construction and application of
Quirk-Schofield diagrams that include pH effects.

Quirk, J. P. (1986) Soil permeability in relation to sodicity and salinity. Phil.
Trans. R. Soc. (London) A3 16:297, and Quirk, J. P. (2001) The significance
of the threshold and turbidity concentrations in relation to sodicity and
microstructure. Aust. J. Soil Res. 39:1185. Two fine salty essays on the
chemistry involved in the reclamation of sodic soils.

Shainberg, I., and J. Letey. (1984) Response of soils to sodic and saline condi-
tions. Hilgardia 52:1. A classic monograph on the physical chemistry and
physics of soil permeability.

Sparks, D. L. (ed.). (1996) Methods of soil analysis: Part 3. Chemical methods.
Soil Science Society of America, Madison, WI. Chapters 14, 15, and 40
of this standard reference describe methods of measuring EC e , SAR, and
calcite solubility.

Sumner, M. E., and R.Naidu (eds.). (1998) Sodic soils. Oxford University Press,
New York. A comprehensive treatise on the causes and management of
sodicity hazard.

Problems

The more difficult problems are indicated by an asterisk.

1. In the table presented here are data pertaining to the saturation extract
of an Aquic Natrusalf. Use these data to calculate the corresponding
equilibrium CO2 pressures, in atmospheres.

EC e Alkalinity EC e Alkalinity

pH (dSrrr 1 ) (mol rrr 3 ) pH (dS rrr 1 ) (mol rrr 3 )

8.05 0.709 1.13 8.25 0.930 1.75

8.10 0.849 1.50 8.30 1.279 1.63

8.20 0.954 1.25 8.35 1.012 1.88

2. In the table presented here are ESP values measured in the upper 0.3 m of
an Alfisol irrigated for 8 years with waters of varying SAR. Use these data
to calculate an average value of K ex for the soil. Take Y ~ 1.3.

Irrigation w

■ater

Gage Canal

Colorado

Sulfate

Chloride

ESP

SAR (mol 1 '' 2 m- 3 ' 2 )

2.1
1.30

3.4
2.92

4.4
4.85

2.7
3.31

Soil Salinity 313

3. Explain conceptually, using Figure 9.2 and Eq. 12.8, why soil structure
may become adversely affected as the Mg + concentration increases in a
soil solution at the expense of Ca 2+ .

4. In a study of soil permeability, it was found that the relationship between
and the ionic strength above which good aggregate soil structure existed
was related to SAR p by

I = 0.6 + 0.56 SARp (0 < SAR p < 32)

where I is in moles per cubic meter, and SAR p is in units of square-root
of moles per cubic meter (mol 1 ' 2 m -3 ' 2 ). Prepare a Quirk-Schofield plot
based on this empirical relationship and Eq. 4.23. Compare your result
with the data plotted in Figure 12.2.

"5. Derive a relationship between [S0 4 _ ] and the ESP of a soil contain-
ing gypsum. Calculate the ESP resulting from c^a
[SO 2- ] = 0.0032 mol dm" 3 using Eq. 12.11. Ignore Mg 2
calculations, but consider ionic strength.

6. The kinetics of dissolution of well-crystallized calcite was observed to
follow the empirical rate law

rateCmolkg"^" 1 ) = 4.14 ±0.46 x 10" 7 (1 - ^) L25±0 - 16

for an initial calcite solids concentration equal to 0.006 kg dm -3 . Estimate
the value of the rate coefficient for calcite precipitation.

7. Derive Eq. 12.34 from Eq. 12.33. Indicate precisely where the assump-
tion (HCO~) e /(Ca 2+ ) e = (HCO~) w /(Ca 2+ ) w is involved in the
derivation.

"8. a. Show that, in the absence of B (OH) 3 , the p.z.c. for a soil adsorbent
described by the constant capacitance model is given by the equation

p.z.c. = - (log K+ - log K_)

[Hint: In the constant capacitance model, the only adsorbed species
are those described by Eq. 12.24 (or Eq. 8.25) and Eq. 12.25.]

b. Application of the constant capacitance model to B adsorption by a
broad group of soils led to average values of K+ and K_ given by

logK+ = 7.29 ± 1.62 logK_ = -10.77 ± 1.26

Estimate the average p.z.c. of the B-adsorbing soil constituents. What
is the likely composition of the soil adsorbent that is interacting with
B(OH)°?

c. What effect will B adsorption have on the p.z.c. of the soils considered
in (b)? (Hint: Apply the third PZC Theorem to Eq. 12.27.)

314 The Chemistry of Soils

d. Use Eq. 12.26 to develop a rationale for the resonance feature near
pH = logKforB(OH)7 protonation (log K = 9.23). (Hint: Combine
eqs. 12.24 and 12.25b, then consider the effect of increasing pH
on each of the two reactants in the resulting B adsorption reaction.)

*9. Goldberg et al. (Goldberg, S., H. S. Forster, and E. L. Heick. (1993) Tem-
perature effects on boron adsorption by reference minerals and soils. Soil
Science 156:316.] have investigated the temperature dependence of the B
adsorption envelope on specimen minerals and arid-zone soils. A variety
of experimental studies indicates that the equilibrium constant for the
overall acid-base reaction obtained by combining Eq. 12.25a with the
reverse of Eq. 12.25b always decreases with increasing temperature.

a. What is the expected temperature dependence of p.z.c?

b. What is the expected temperature dependence of the resonance
feature in the B adsorption envelope? Does this expectation agree
with the observations of Goldberg et al. (1993)?

*10. Goldberg et al. [Goldberg, S., S. M. Lesch, and D. L. Suarez (2000)
Predicting boron adsorption by soils using soil chemical parameters in
the constant capacitance model. Soil Sci. Soc. Am. J. 64:1356.] derived
Eq. 12.28 for a variety of soils representing six different soil orders. Cal-
culate Kb for Diablo clay (a Vertisol), given f oc = 19.8 g kg - , fj oc =
0.26gkg _1 ,Al = 1.02 g kg" 1 , and a s = 0.19m 2 g _1 . If [SOH] =
3.1 x 10 _4 moldm~ , calculate the concentration of =SOB(OH)^~ that
is in equilibrium with a B(OH)3 concentration at the maximum permit-
ted for unrestricted use of irrigation water with respect to boron toxicity
hazard. Take pH = p.z.c. = 9.47 for this soil. Convert your result to an
amount adsorbed in micromoles per gram given c s = 200 kg m _ as the
solids concentration.

1 1 . Given the following table of EC W values, indicate which irrigation waters
are likely to result in a saline root zone if a leaching fraction of 0.2 is used.
What maximum SAR pw values would be acceptable for these waters?

River water EC W (dS m 1 )
Salt Colorado Sevier

1.56 1.27 2.03

12. Give a rationale for why the equation

SARdw = (CNaw/LF) /

(cMgw/LF) + c£

Soil Salinity 315

should provide a reasonably accurate estimate of the SAR value for water
draining from the root zone. Explain carefully why LF appears in the
equation and why c^? is used.

13. Gypsum is applied to a soil irrigated with water in which EC W =
1.3 dSm - . Given that CNa = 12molm _ , CMg = 5.2molm~ , and
[S0 4 ~] = 0.014 mol dm - in the soil solution at steady state, calculate
the steady-state ESP in the soil if the leaching fraction is 0.20.

*14. Evaluate the factor within curly brackets in Eq. 12.35 for K so =
10~ 8 ,I = 20molm~ 3 , and [HCO~] w /[Ca 2+ ] w = 1.0, after convert-
ing the equation to an expression for c<-? using xhco 3 and yea- Compare
your result with the appropriate entry in Table 1 of Suarez [Suarez, D.
(1981) Relation between pH c and sodium adsorption ratio (SAR) and an
alternative method of estimating SAR of soil or drainage waters. Soil Sri.
Soc. Am.}. 45:469.]

15. The Colorado River irrigation water referred to in Problem 11 has
EC W = 1.3 dSm _1 ,[HCO~]/[Ca 2+ ] = 1.12, c Naw = 5 mol m" 3 , and
CMgw =1.3 mol m _ . Calculate the value of adj RNa for this water using
Eq. 12.35 using K so ~ 10 -8 and Pco 2 = 10 -3 ' 15 atm. Compare your
result with the value of SAR based on ccaw = 2.6 mol m _ .

Appendix: Units and Physical Constants
in Soil Chemistry

The chemical properties of soils are measured in units related to le Systeme
International d'Unites, abbreviated SI. This system of units is organized around
seven base physical quantities, six of which are listed in Table A. 1. (The seventh
base physical quantity, luminous intensity, is seldom used in soil chemistry.)
The definitions of the SI units of the base physical quantities have been
established by international agreement.

One meter is a length equal to 1,650,763.73 wavelengths in vacuum of the
radiation corresponding to the transition between the levels 2pio and 3ds in
86 Kr.

One kilogram is the mass of the international metal prototype mass
reference.

Table A.1

Base units in the Systeme International.

Property SI unit Symbol

Length

meter

Mass

kilogram

Time

second

Electric current

ampere

Temperature

kelvin

Amount of substance

mole

mol

316

Appendix: Units and Physical Constants in Soil Chemistry 317

One second is the duration of 9,192,631,770 periods of the radiation cor-
responding to the transition between two hyperfine levels of the ground state
in 133 Cs.

One ampere is the electric current that, if maintained constant in two
straight, parallel conductors, of infinite length and negligible cross-section,
and placed 1 mm apart in vacuum, would produce between them a force of
0.2 |xN per meter of length.

One kelvin is 1/263.16 of the absolute temperature at which water vapor,
liquid water, and ice coexist at equilibrium (the triple point) .

One mole is the amount of any substance that contains as many elementary
particles as there are atoms in 0.012 kg of 12 C.

Fractions and multiples of the SI base units are assigned conventional
prefixes, as indicated in Table A.2. Thus, for example, 0.1 m = 1 dm, 0.01
m = 1 cm, 10 -3 m = 1 mm, 10 -6 m = 1 |im (not 1 |x!), and 10 -9 m = 1 nm.
An exception to this procedure is made for the unit of mass, because it already
contains the prefix kilo. Fractions and multiples of the kilogram are denoted
by adding the appropriate prefix to the mass in units of grams. For example,
10~ 6 kg = 1 mg, not 1 ixkg, and 10 3 kg = 1 Mg, not 1 kkg.

Several important units of measure are defined directly in terms of the SI
base units. The time units, minute (1 min = 60 s), hour (1 h = 3600 s), and
day (1 d = 86,400 s), are examples, as are the liter (1 L = 1 dm ), the coulomb
(the quantity of electric charge transferred by a current of 1 A during 1 s),
and degrees Celsius (°C), which is equal to the temperature in kelvins minus
273.15. The pressure units, atmosphere (1 atm = 101.325 kPa) and bar (1 bar
= 10 5 Pa), are common alternatives in the laboratory to the small SI unit,
pascal (Pa). Other important units related to the SI base units are listed in
Table A.3.

The unit mole is closely related to the concept of relative molecular mass,

M r . The relative molecular mass of a substance of definite composition is

the ratio of the mass of 1 mol of the substance to the mass of 1/12 mol of

C (i.e., 0.001 kg). Although M r is a dimensionless ratio, it is conventionally

designated in daltons (Da). For example, the relative molecular mass of H2O

Table A.2

Prefixes for units in the Systeme International.

Fraction

Prefix

Symbol

Multi

pie

Prefix

Symbol

10- 1

deci

deca

10- 2

centi

10 2

hecto

10- 3

milli

10 3

kilo

1(T 6

micro

10 6

mega

10- 9

nano

10 9

giga

1(T 12

pico

10 12

tera

318 The Chemistry of Soils

(I) is 18.015 Da, which means that the absolute mass of 1 mol water is 0.018015
kg. The relative molecular mass of the smectite montmorillonite, with the
chemical formula Nao.glSiygAlo^lAbj.sMgo.sC^f^OH)^ is the weighted sum
of M r for each element in the solid: 0.9 x 22.990 (Na) + 7.6 x 28.086 (Si) +
3.9 x 26.982 (Al) + 0.5 x 24.305 (Mg) + 24 x 15.999 (O) + 4 x 1.0079 (H)
= 739.54 Da. The same method of calculation applies to any other substance
of known composition.

The SI unit of concentration is moles per cubic meter, which is equal
numerically to millimoles per liter. The unit molality is preferred for mea-
surements made at several temperatures, because it is a ratio of the amount
of substance to the mass of solvent, neither of which is affected by changes in
temperature. The concentration of adsorbed charge in a soil is measured in
moles of charge per kilogram soil (Table A. 3). For example, if a soil contains
49 mmol adsorbed Ca kg -1 , then it also contains 0.098 mol c kg -1 contributed

Table A.3

Units related to SI base units.

Property

Unit

Symbol

SI relation

Area

hectare

10 4 m 2

Charge concentration

moles of charge
per cubic meter

mol c m~ 3

Concentration

moles per cubic
meter

mol m

Electric capacitance

farad

m- 2 kg- 1 s 4 A 2

Electric charge

coulomb

Electric potential difference

volt

m 2 kgs~ 3 A -1

Electric conductivity

Siemens per meter

SnT 1

m _3 kg _1 s 3 A 2

Energy

joule

m 2 kg s~ 2

Force

newton

m kg s

Mass density

kilogram per cubic
meter

kg m~ 3

Molality

moles per kilogram
of solvent

mol kg~

Pressure

pascal

m _1 kg s~ 2

Relative molecular mass

dalton

Specific adsorbed charge 3

moles of charge
per kilogram of
adsorbent

mol c kg

Specific surface area 3

hectare per
kilogram

ha kg" 1

10 4 m 2 kg- 1

Viscosity

newton-second per

NsirT 2

square meter

Volume

liter

1(T 3 m 3

a Specific means "divided by mass

Appendix: Units and Physical Constants in Soil Chemistry 319

Table A.4

Values of selected physical constants.

Name Symbol Value

Atmospheric pressure Po 101.325 kPa (exactly)

Atomic mass unit 3 u 1.6605 x 10 -27 kg

Avogadro constant N A , L 6.0221 x 10 23 mol -1

Boltzmann constant k B) k 1.3807 x 10~ 23 J KT 1

Faraday constant F 9.6485 x 10 4 C mol -1

Molar gas constant R 8.3 145 J K~ : mol" '

Permittivity of vacuum s 8.8542 x 10~ 12 C 2 J" 1

Zero of the Celsius temperature scale To 273.15 K (exactly)

a 1 u is defined numerically by the ratio 0.001 kg/NA.

by adsorbed Ca. In general, as discussed in Chapter 9, the moles of adsorbed
charge equal the absolute value of the valence of the adsorbed ion times the
number of moles of adsorbed ion per kilogram soil. The cation exchange
capacity (or CEC) of a soil is expressed in the units of specific adsorbed charge.
In a similar manner, the concentration of ion charge in a soil solution (Q) is
measured in moles of charge per cubic meter (mol c m -3 ) and is equal numer-
ically to the absolute value of the ion valence times the ion concentration in
moles per cubic meter.

The values of the most important physical constants used in soil chemistry
are listed in Table A.4. These fundamental constants appear in theories of
molecular behavior in soils. Note that R = Na1<b and that F = Nac, where e is
the elementary charge.

For Further Reading

Cohen, E.R. et al. (2007) Quantities, units and symbols in physical chemistry.
3rd edition. RSC Publishing, Cambridge, UK. The standard reference for
units of measure and definitions based on the Systeme International. It is
available in an online version at http://goldbook.iupac.org.

Problems

1. Show that a pascal is the same as a force of 1 N acting on 1 m 2 . (Hint: Use
Table A. 3 to express pascals in terms of newtons.)

2. Using the information in Table A. 3, show that a volt is the same as a joule
per coulomb. Calculate the electrode potential scale factor, RT/F (Eq. 6.18),
in volts at 298.15 K. (Answer: 0.025693 V)

320 The Chemistry of Soils

3. Use the data in Table A.4 to calculate the mass of Na atoms of C. (Answer:
0.012 kg)

4. Calculate the relative molecular mass of a Ca-vermiculite having the chem-
ical formula Cao.7[Si 6 .6Ali.4]Al 4 02o(OH)4. [Answer: M r = 0.7 (40.078) +
6.6 (28.086) + 5.4 (26.982) + 24 (15.999) + 4 (1.0079) = 747 Da]

5. Calculate the relative molecular mass of a fulvic acid "molecule" with the
chemical formula C186H245O142N9S2. [Answer: M r = 186 (12.011) + 245
(1.0079) + 142 (15.999) + 9 (14.007) + 2 (32.066) = 4943 Da]

6. Calculate the mass of 1 mol humic acid with the chemical formula
C185H191O90N10S. (Answer: 4.027 kg)

7. Use the result of Problem 6 to calculate the concentration of humic acid in
a solution containing 0.5 g humic acid L _1 . (Answer: 0.1242 mol m -3 =
124.2 \iM)

8. Ten milliliters of soil solution contain 5.5 mg CaCi2. Calculate the con-
centration of CaCi2 and the charge concentration of Cl _ in the solution
assuming complete dissociation. (Answer: The concentration of CaCi2 is
4.96 molm -3 , and the charge concentration of Cl _ is 9.92 mol c m _3 .Note
that 49.6 [xraol CaCi2 is dissolved in the 10 mL water.)

9. Given that the mass density of liquid water is 997 kg m -3 , calculate the
molality of CaCi2 in the solution described in Problem 8. (Hint: Derive the
following relation: concentration = molality x mass density of solvent.)

10. Calculate the adsorbed charge of Ca on the vermiculite with the chem-
ical formula given in Problem 4. (Hint: What is the mass of 1 mol
Ca-vermiculite? How many moles of Ca charge does 1 mol of the clay
mineral contain? Answer: 1.87 mol c kg .)

Index

Absolute temperature, 317
Acetic acid, 66

Acid-neutralizing capacity, 77, 117, 276,
279, 289

buffer intensity, 77, 277

exchangeable aluminum, 286

humus, 77, 276, 280

lime requirement, 288

NICA-Donnan model, 277

relation to cation exchange capacity,
276,279

relation to redox reactions, 153, 286

relation to total acidity, 77, 276, 279

soil minerals, 286

soil solution, 279
Acidic soil, 275

aluminum geochemistry, 126, 282

carbonic acid, 276

exchangeable acidity, 279

humus, 276

nutrient bioavailability, 288

proton cycling, 275

redox reactions, 286
Activity, 110, 123

aqueous species, 110

bioavailable species, 7, 231

electron, 151

exchangeable species, 229, 290

gas species (partial pressure), 136, 149,
152, 158

ideal solution, 132, 229

ion activity product, 123

liquid water, 133, 141,284

proton, 116, 151, 276, 293, 304

solid species, 123, 130
Activity coefficient, 110, 307

Davies equation, 111

neutral complex, 112

surface complex, 307
Activity- ratio diagram, 125

aluminum minerals, 129, 283

calcium phosphates, 138

clay minerals, 129, 142, 283
Acute toxicity, 230
Adsorbate, 179

Adsorbed charge, 182, 220, 222, 318
Adsorbent, 179
Adsorption, 15, 179

anion, 206

defined, 179

effect on colloidal stability, 254, 257, 261

isotherm, 198

kinetics, 197

measurement, 179, 195

mechanisms, 179

metal cation, 203

321

322 Index

Adsorption (continued)

models, 200, 206, 306

negative, 179

nonspecific, 180

relation to precipitation, 203

specific, 180

surface excess, 195
Adsorption edge, 205
Adsorption envelope, 208
Adsorption isotherm, 198

classification, 199

Langmuir, 200

Langmuir-Freundlich, 202, 234

van Bemmelen-Freundlich, 203
Adsorption models, 200, 206, 234, 306
Adsorptive, 179

Affinity parameter, 200, 202, 234
Aggregation, 43, 46, 245
Aliphatic acid, 66

formation by carbon dioxide
reduction, 149
Alkalinity, 117,280,297

acidic soil, 281

carbonate, 117

redox effects, 286

saline soil, 297
Allophane, 12, 47

chemical formula, 47

point of zero net proton charge, 47

reactions with humus, 84

structure, 47

weathering, 48, 59, 142
Aluminum geochemistry, 282

aqueous species, 108,281

cation exchange, 285, 289, 292

liming, 289

minerals, 43, 47, 49, 56

solubility, 129, 132,283
Aluminum hydroxy polymers, 46, 278

on clay minerals, 46, 48
Amide group, 72
Amino acid, 68

formation by carbon dioxide
reduction, 150
Ammonia volatilization, 6
Ampere, 317

Amphibole, 13,37,40, 122
Anion adsorption, 207

pH effect, 189,208
Anion exchange capacity, 222
Anion exclusion, 206
Anion polyhedra, 29

radius ratio, 33

Anoxic soil, 153

Anthropogenic mobilization factor, 8

Apatite, 56, 130, 136

Arid-zone soil, 296

Aromaticity, 14

Arrhenius equation, 115

Assimilatory reduction, 154

Atomic mass unit, 319

Atmosphere, 317

Avogadro constant, 319

Background electrolyte, 74
Barium exchange method, 23, 73, 239
Basaluminite, 56
Beidellite, 45

formation, 41

weathering, 48
Bicarbonate, 25, 116

acidic soils, 276

alkalinity, 117,280,297

equilibria, 116,297,304

saline soils, 298, 304
Biotic ligand model, 230
Biotite,37,39,59
Binary cation exchange, 223
Birnessite, 12, 53, 57

reductive dissolution, 152, 157

structure, 53, 57
Black carbon, 70
Bond strength, 29
Bond valence, 33
Borate minerals, 305
Boron adsorption, 189, 208, 306
Boron geochemistry, 305
Boron toxicity, 305
Bridging complexation, 82
Brownian motion, 245
Buffer intensity, 77, 277

humus, 77, 88,278

soil, 277

Calcareous soil, 54, 135
Calcite, 12, 54

dissolution rate, 303, 313

lime requirement, 288

phosphate solubility, 135, 143

precipitation rate, 140, 303

relation to sodium adsorption ratio,
299,310

solubility, 135, 303

supersaturation, 304
Calcium -aluminum cation exchange, 285

lime requirement, 289

Index 323

Calcium phosphates, 135
Calomel electrode, 293
Carbohydrate, 69
Carbon corrosion, 162
Carbon dioxide, 5, 16, 25, 276

activity (partial presure), 117

bicarbonate formation, 116

dissolved, 17,25,98,116

in soil air, 16, 24, 276

reduction, 150, 156

relation to pH, 117,276

relative saturation of calcite, 136

siderite formation, 163

solvated,25,98
Carbon-to-nitrogen ratio, 5, 13, 82
Carbonate, 54

alkalinity, 117

solubility, 163, 303

speciation, 116,297
Carbonic acid, 25, 55, 135, 276

dissociation, 55, 116, 135

neutral species, 25, 98

soil acidity, 276

solvated carbon dioxide, 25

speciation, 116,297
Carboxyl group, 156

humic substances, 72

ligand exchange reaction, 84
Carboxylate, 9, 66, 84

ligand exchange reaction, 84
Cation bridging, 83, 176
Cation exchange, 72, 219, 228, 233

biotic ligand model, 232

humus, 72, 233

kinetics, 74,91,227

selectivity, 228
Cation exchange capacity, 219

acidic soils, 221,276

clay minerals, 46, 221

correlation with humus content, 221

humus, 73, 235

layer charge, 45

measurement, 73, 181,219,239

relation to total acidity, 88, 276, 279

surface soils, 221

units, 319
Cation exchange kinetics, 74, 91, 227
Cation exchange selectivity coefficient, 228
C-curve isotherm, 199
Cellulose, 69
Celsius temperature, 317
Charge fraction, 223
Charge screening, 180, 253

Charge -transfer complex, 78
Chelate, 96

Chemical elements in plants, 13, 22
Chemical elements in soils, 4

anthropogenic mobilization factor, 4, 8

compared to earth crust, 4

essential, 5,22

macronutrient, 5

major, 5

trace, 5

variability, 3
Chemical reactions, 25

charge balance, 26, 169

ion exchange, 226

ligand exchange, 207

mass balance, 26, 169

redox, 151, 169
Chemical species, 98

acidic soil, 108

redox, 148, 151

saline soil, 297

surface, 174
Chlorinated ethenes, 167

Chlorite, 43

defined, 47

pedogenic, 46, 59
Chloritized smectite, 46, 48
Chloritized vermiculite, 43, 46
Clay mineral, 18, 41

aggregates, 43, 46

flocculation, 248

groups, 43

isomorphic substitution, 45

layer types, 43

proton charge, 44

reactions with humus, 83

structural charge, 45

weathering, 19,48
Coagulation, 245

critical concentration, 253, 257

kinetics, 245, 248, 262
Colloid, 244
Colloidal stability, 244, 255

adsorption effects, 261

critical coagulation concentration, 254

electrolyte concentration effect, 254, 261

polymer effect, 261
Complex, 96

aqueous, 98

inner-sphere, 97

kinetics of formation, 98, 115

outer-sphere, 97

solvation, 97

324 Index

Complex (continued)

stability constant, 102, 105, 110

surface, 176,207,212
Complexation, 20, 82,96, 102, 105,212
Complexation kinetics, 98
Concentration, 318
Condensation polymer, 67, 69, 284
Conditional exchange constant, 228

relation to equilibrium constant, 229
Conditional solubility product, 125
Conditional stability constant, 105

relation to equilibrium constant, 111

surface complexes, 306
Congruent dissolution, 19, 134
Constant capacitance model, 306
Coordination number, 29

Pauling rules, 33

principal, 30
Coprecipitation, 14, 130
Corundum, 36, 178
Coulomb, 317
Covalent bond, 28
Critical coagulation concentration, 253

model, 254

relation to sodium adsorption ratio, 300

soil particles, 254, 270

stability ratio, 257
Crystalline mineral, 43
Cycle, bio geo chemical, 5

proton, 275

residence time, 22

Dalton,317

Denitrification, 6, 286

Denticity, 96

Diffuse double layer, 207, 216, 235, 253

electrostatic force, 253

exclusion volume, 216, 243

screening parameter, 253

surface charge, 182
Diffuse-ion swarm, 180
Diffusion coeficient, 91, 245, 267
Diffusion time constant, 93, 248
Dioctahedral sheet, 38
Disperse suspension, 244
Disproportionation, 157
Dissimilatory reduction, 154
Dissolution reaction, 119

equilibrium constant, 123

ion activity product, 123

intrinsic timescale, 58, 121

kinetics, 120

mechanisms, 120

surface control, 120

transport control, 120
Distribution coefficient, 102, 200, 205

adsorption, 200

Chiou,81

Langmuir equation, 201

speciation equilibria, 102
Diaspore,58, 131
Dolomite, 54
Dryfall, 275

Easily weathered minerals, 12, 37, 41

effect on colloidal stability, 303

Si-to-O ratio, 122
Electrode potential, 158
Electrolyte conductivity, 318

definition of saline soil, 296

ionic strength, 111

leaching fraaction, 309

Quirk-Scho field diagram, 301

salinity and sodicity hazards, 302, 308
Electrolyte, 16
Electron activity (pE), 151
Electrostatic force, 253
Equilibrium constant, 110

cation exchange, 229, 289

complex formation, 110

mineral dissolution, 122

reduction half- reaction, 151

surface complex formation, 306
Exchange isotherm, 223

nonpreference, 223, 225, 229, 285
Exchangeable acidity, 277, 279
Exchangeable aluminum, 279, 289
Exchangeable ions, 180,219

acidic soils, 222, 279, 292

alkaline soils, 222, 298

molecular definition, 180

Schindler diagram, 188
Exchangeable sodium percentage, 299
Exclusion volume, 207, 216, 235,243,

253,268
Extent of diffuse double layer, 253

Farad, 318

Faraday constant, 319

Feldspar, 12,37,39

structure, 38

weathering, 25, 40, 54, 59, 140, 141
Fermentation, 145
Ferrihydrite, 12, 52, 163

structure, 52
Fick's law, 9 1

Index 325

Film diffusion, 74,91, 116

cation exchange kinetics, 74, 91, 227
Flocculation,245,257
Floccules,248,261
Flooded soils, 144

reduction sequence, 145, 160
Flux, 91

composition, 95
Fractal, 263, 271

dimension, 263, 273

floccule, 261
Free-ion species, 8, 36, 97, 109
Fulvic acid, 13,70

composition, 13, 24, 72, 320

functional group acidity, 72

proton complexation, 74, 235

structure, 72
Functional group, 68, 72

humus, 72

surface, 174

Gay— Lussac-Ostwald step rule, 128, 141, 282
Geosymbiotic, 48, 54
Gibbsite, 49

dissolution, 120, 124

ion activity product, 123

solubility, 123, 128, 132,284

structure, 50

"window", 127, 142,283
Glass electrode, 171, 293
Goethite, 51

hydrogen bonds, 34

isomorphic substitution, 58, 131

reductive dissolution, 148, 210

structure, 35, 50, 57
Green rust, 52, 55, 167,211
Gypsum, 55

acidic soils, 122

dissolution, 59, 122

saline soils, 303, 313

solubility, 123, 303

Half-life, 100

coagulation, 248

diffusion, 93

relation to rate coefficient, 101
Halloysite, 44

association with allophane, 48
Hamaker constant, 252
H-curve isotherm, 199
Hectare, 46, 318
Hematite, 51

flocculation, 256, 258, 259, 270

Henry's law, 16, 24
Humic acid, 13, 70

cation exchange, 73, 236

composition, 13, 24, 72, 320

functional group acidity, 72

proton complexation, 76, 87, 235, 277
Humic substances, 13, 70

composition, 24, 71

defined, 13

formation, 65, 70

functional groups, 72

structure, 72

supramolecular association, 71, 86
Humification, 5
Humus, 5

acid-neutralizing capacity, 77, 87, 277

buffer intensity, 77, 277

cation exchange reactions, 72, 233

metal complexes, 108

reactions with organic compounds, 77

reactions with soil minerals, 82, 90

recalcitrant, 90

residence time, 22

total acidity, 88
Hydrogen bonds, 35, 71
Hydrolysis, 19, 188

effect on metal cation adsorption,
206, 228

ionic potential, 8
Hydrophobic effect, 79
Hydrophobic interaction, 72, 79
Hydroxycarbonate minerals, 55

Ideal gas law, 24
Illite,43,45

floccules, 249

structure, 42
Imogolite, 47, 142
Incongruent dissolution, 19
Indifferent electrolyte, 187, 256
Inner-sphere surface complex charge, 182
Interflow, 275
Interparticle forces, 250
Intrinisc surface charge, 182
Ion activity product, 123
Ion exchange capacity, 219
Ion exchange reactions, 226
Ion polaraizability, 9
Ionic bond, 28

strength, 29

valence, 33
Ionic potential, 8, 29

relation to toxicity, 10

326 Index

Ionic radius, 29

metal cations, 32

oxygen, 29

relation to metal ion adsorption, 228
Ionic strength, 111

Marion-Babcock equation, 111

saline soil, 296, 309, 313
Index ions, 219
Iron plaque, 51
Iron reduction, 148, 157

pE-pH diagram, 163

poising, 161
Irrigation water quality, 308

Quirk-Schofield, diagram, 301

salinity and sodicity hazards, 308
Irving— Williams sequence, 204
Isomorphic substitution, 13

allophane, 47, 59

clay minerals, 43

feldspars, 40

goethite,58, 131

illite, 43

kaolinite,43, 58

mica, 38

layer charge, 45

smectite, 45

vermiculite, 43

Jackson-Sherman weathering stages, 18
Jarosite, 56
Jurbanite, 56, 59

Kaolinite, 43

defined, 43

flocculation, 267, 270

isomorphic substitution, 58

solubility, 121, 127, 133, 140,283

structure, 42

surface charge, 44

"window", 127, 283
Kelvin, 317
Kilogram, 316
Kurbatov plot, 205

Langlier index, 304

Langmuir equation, 200

Langmuir-Freundlich equation, 202, 234

Layer charge, 45

L-curve isotherm, 198

Leaching fraction, 309

Lewis acid, 175

Lewis acid site, 174, 207

Ligand exchange, 84, 175

general reaction, 207
Light scattering, 269
Lime potential, 289
Lime requirement, 288
Liquid junction potential, 294
Lithiophorite, 12, 49, 64

Macronutrient, 5

Maghemite, 52

Magnesian calcite, 54, 58

Magnetite, 52

Major element, 5

Manganese reduction, 144, 150

pE— pH diagram, 169

poising, 157, 169
Marcus process, 212
Marion-Babcock equation, 111
Metal cation adsorption, 203

effect of pH, 189,205

effect on colloidal stability, 261
Metal hydroxides and oxides, 49

point of zero net charge, 186

structures, 50, 57
Meter, 316

Methane, 5, 17, 144, 150, 158
Mica, 12, 38

structure, 38

weathering, 39, 59
Microbial catalysis, 148, 153
Mineral weathering, 17, 119, 302

complexation, 20

hydrolysis and protonation, 19

Jackson-Sherman stages, 18

oxidation, 19,211

reduction, 210

soil acidity, 276, 278, 282

soil salinity, 302
Molality, 318
Molar gas constant, 319
Mole, 317
Mole fraction, 230
Moles of charge, 318
Monosaccharide, 69
Montmorillonite, 43

defined, 45

floccule, 249

relative molecular mass, 318

structural charge, 45

structure, 42

Negative adsorption, 179, 196, 206, 220
Nernstfilm, 91

Index 327

Net proton charge, 75, 182
NICA-Donnan model, 234, 243, 277
Nitrate reduction, 6, 147, 152, 160

flooded soil, 145

half-reactions, 150

nitrite formation, 150

soil acidity, 286
Nitrate respiration, 160
Nitrogen fertilizer, 287
Nitrogen oxides, 6, 150

dissolved, 17

flooded soil, 286
Number density, 248, 273

Ocatacalcium phosphate, 56, 136
Octahedral sheet, 36
Olivine, 37, 122, 170
Open system, 3 275

"free-body cut" 1 10
Order, reaction, 99
Orthokinetic flocculation, 245
Outer-sphere surface complex charge, 182
Oxalic acid, 66
Oxic soil, 152
Oxidant, 148
Oxidation, 19

Oxidation number, 149, 169
Oxidation-reduction reaction, 148, 150

balanced, 169

kinetics, 153
Oxyanion, 8
Oxygen reduction, 146, 152

electrochemical measurement, 171, 293
pH 50 ,205,208,216
Phase, 94

Phenolic hydroxy!, 67, 72, 235
Phosphate adsorption, 20 1, 208
Phosphate fertilizer, 135
Point of zero charge, 183, 186, 257, 313

colloidal stability, 257, 261

general properties, 186, 188, 313
Point of zero net charge, 186

relation to point of zero charge, 187

Schindler diagram, 188

soil minerals, 186
Point of zero net proton charge, 184

relation to point of zero net charge, 186
Point of zero salt effect, 185
Poising, 156, 160
Polymer bridging, 261
Polymorph, 157
Polysaccharide, 69
Poorly crystalline mineral, 43, 90
Potassium fixation, 177
Primary minerals, 1 1
Primary particles, 261
Primary silicates, 36

structures, 38

weathering, 18,41
Protein, 67
Proton cycling, 275
Protonation, 8, 75, 120, 182, 189
Pyroxene, 13, 37, 122
PZC theorems, 186

Partial order, reaction, 99
Pascal, 318
Pauling rules, 33
pE value, 151

electrochemical measurement, 158

oxygen pressure, 157

microbial ecology, 161

poising, 156

redox ladder, 159

reduction sequence, 160
pE— pH diagram, 162
Pedogenic chlorite, 46
Peptide, 67

Perikinetic flocculation, 245, 255
Permittivity of vacuum, 319
pH value, 1 16, 152, 276, 294, 304

acidic soil, 275

carbonic dioxide, 276

compared to pE, 152

Quartz, 12, 37

solubility, 128,283

structure, 38

weathering, 18, 38, 122, 141
Quirk-Scho field diagram, 300

Radius ratio, 34

Rate coefficient, 92, 99

adsorption, 200

backward, 99

coagulation, 248

complexation, 99, 115

dissolution, 120, 125

film diffusion, 92

forward, 99

pseudo, 99

relation to equilibrium constant, 100,
125,200,228

relation to half-life, 101

328 Index

Rate law, 99

Fick,91

von Smoluchowski, 248
Reaction kinetics, 101

first order, 101

second order, 101, 248

zero order, 101, 120
Redox, 6, 148, 157, 169,209

couple, 151

ladder, 154, 159

surface, 211
Redox buffer, 156
Reductant, 148
Reduction half-reaction, 148, 150

general example, 151

proton consumption, 153

role in balalncing redox reactions, 149

sequence in soils, 145, 160
Reductive dissolution, 210
Relative molecular mass, 317

clay minerals, 45, 318, 320

fulvic acid, 320

humic acid, 320
Relative saturation, 124

calcite, 140, 304

gibbsite, 124
Residence time, 22
Resident composition, 95
Resistant soil minerals, 12
Rhizosphere,20,21,23, 143

nutrient uptake, 278

pH value, 279, 287

Saline soil, 296
Salinity hazard, 308
Salinity-sodicity relation, 301, 308
Salt bridge, 294
Saturation extract, 95, 296
Schindler diagram, 188, 206, 208
Schulze— Hardy rule, 254
Schwertmannite, 56, 59
Scofield dilution rule, 226
S-curve isotherm, 198
Second, 317
Secondary minerals, 13
Siderophore, 68, 167
Selectivity sequence, 204
Sheet, 35

Siderite,55, 163, 169
Silicic acid, 16
Siloxane cavity, 36, 175
Siloxane surface, 175

Smectite, 12,43

defined, 43

floccule, 249

structural charge, 45

structure, 42

weathering, 18,48, 127, 135
Sodic soil, 300, 302, 308
Sodicity hazard, 308
Sodium adsorption ratio, 299

practical, 300

relation to exchangeable sodium
percentage, 299

Quirk-Scho field diagram, 301

sodic soil, 300, 302

sodicity hazard, 308

Suarez,310,315
Sodium -calcium exchange, 196,225,

229,298
Soil adsorbent, 226
Soil air, 16

carbon dioxide, 16, 24

oxygen, 16, 152
Soil chemical composition, 3
Soil colloids, 248
Soil horizon, 3
Soil minerals, 28
Soil organic matter (humus), 5

acid-neutralizing capacity, 77, 277

age, 22

alkalinity, 280

biomolecules, 65, 72

buffer intensity, 77, 277

cation exchange, 72

climate effect, 5, 21

humic substances, 13, 70

humification, 5

humin, 70

pools, 5

reactions with minerals, 82

reactions with organic molecules, 77

supramolecular structure, 71
Soil respiration, 22
Soil solution, 5, 94

acid-neutralizing capacity, 281

extraction, 95

salinity, 296
Solid solution, 15, 58, 131, 225, 229
Solubility, organic compounds, 80, 88
Solubility product constant, 123

conditional, 125
solvation complex, 97
Sorption, 180,203

Index 329

Speciation, 16, 101,104

Aridisol, 297

mass balance, 102, 105

metal, 98

prediction, 104, 114

Spodosol, 108
Specific adsorption, 180, 188, 306
Specific surface area, 43, 46, 49, 51, 52, 54, 318
Stable suspension, 244

surface chemical factors, 261
Stability constant, 105
Stability ratio, 255
Stern layer, 180, 182, 187
Stoichiometric saturation, 131
Stokes-Ein stein model, 245, 267
Structural charge, 45, 181, 186
Suboxic soil, 152
Sulfate reduction, 145, 155

equilibria, 158, 166, 169

half-reactions, 150
Sulfide, 155

anoxic soils, 158

pE— pH diagram, 169
Surface charge, 181
Surface charge balalnce, 183
Surface complex, 176

anions, 178, 306

binuclear, 179

effect on point of zero charge, 188

inner-sphere, 176

metal cations, 177, 178, 250

multinuclear, 181

outer-sphere, 176

ternary, 176
Surface excess, 195
Surface functional group, 174
Surface hydroxyl, 1 75

birnessite, 57

gibbsite, 50, 120

goethite, 50, 57

kaolinite, 44

Taube process, 212

Terminal electron-accepting process, 158

Ternary cation exchange, 223
Ternary surface complex, 176
Tetrahedral sheet, 35

structure, 36
Thermal screening length, 254
Thermodynamic exchange constant,
229,289

conditional constant, 228
Thermodynamic stability constant, 110

conditional constant, 111
Titration, 74
Total acidity, 88, 276, 279

optimum value, 288

relation to cation exchange capacity,
88, 279
Total particle charge, 182, 186, 261
Trace element, 5
Trioctahedral sheet, 38
Trona, 54, 59
Turbidity, 269

Valence, 31

bond, 33

metals, 31

oxidation number, 169

role in adsorption, 228
van Bemmelen-Freundlich equation, 203
van der Waals interaction, 78, 252
Vanselow model, 229, 299
Vermiculite, 12,45

chloritized, 46

defined, 43

hydroxy- interlayer, 45, 46, 48

structural charge, 46

weathering, 18,48
Vernadite, 53
von Smoluchowski rate law, 248

Water bridging, 83, 176
Water ionization product, 103
Water quality criteria, 308
Water quality standards, 308
Wetfall,275